Not Applicable.
Not Applicable.
1. Field of Invention
This invention relates to piano key mechanisms, and more specifically to improvements in measuring the performance characteristics of key mechanisms of a piano or keyboard.
2. Background Art
As an aid to the following prior art discussion, a brief description of the two basic piano actions follows.
Also shown in
We refer next to
Traditionally, the “static feel” of the key mechanism (also known as the key action) of a piano is measured by a process of gradually adding or subtracting “gram weights” to/from the front end of the key, until key movement ensues. This is generally done with the sustain pedal depressed or otherwise disengaged, so that the damper lever resistance is no longer encountered in the stroke. The weights are typically placed 10 to 12 mm from the front edge of the key. This will be known as the Application Point (AP). The two quantities directly measured in this longstanding process are:
The quantity (i) is typically referred to as Down Weight (DW), while (ii) is called the Up Weight (UW). Both parameters are functions of gravity forces acting on the mechanism, various spring forces, friction at various points in the mechanism, and in some cases magnetic forces. DW is often used as the indicator in attempting to ensure a constant (or continuous) touch resistance across the keyboard. One of the main purposes for measuring the DW and UW is to determine still two other parameters: Balance Weight (BW) and Friction. The Balance Weight (BW) is simply the average of DW and UW. Balance Weight has the benefit of being theoretically independent of the friction in the key action. Ideally, it expresses the combined effects (at the Application Point, AP) of all the “static” force components of the mechanism (springs, gravity, magnets) except friction. For this reason, it is generally considered better to use BW, rather than DW, as the guiding parameter, when attempting to achieve a constant or continuous touch resistance across the keyboard. Friction in the key mechanism is notorious for changing quickly and randomly over time. This is usually due to warpage, shrinkage or expansion of component parts. And all this is made worse when either the humidity or temperature varies severely over time. Therefore, the fastidious piano technician has the goal of trying to ensure that the BW's of all the keys are either constant, or at least vary in a continuous manner from key to key. Regarding Friction, it is also obtained from DW and UW. Calculated Friction is simply half of the difference between DW and UW.
If the BW measurement (often DW is used to save time) is not within some specification, the remedy is often the embedding of small, lead weights (called keyleads) into the wooden keys. On a grand piano, they are usually placed in front of the balance rail. Three of them are shown in
It should be noted that the above Prior Art methods of measuring the “feel” of the piano keys neglect that portion of the resistance due to inertia. These inertia forces are indeed felt whenever the key (and associated mechanism) is accelerated. So the type of feel that these long-used methods attempt to address is related to relatively soft playing, where acceleration is either minimal or short-lived. From hereon, I will refer to this “feel” as the Static Resistance of the key mechanism.
With regards to this longstanding practice of measuring the static values of Down Weight, Up Weight, and (indirectly) Balance Weight, the process is very tedious and time-consuming. Largely because of this, it is prone to operator error. In addition, it is prone to error just by nature of the process itself. As I will demonstrate below, the effects that the process is supposed to quantify (gravitational, magnetic, spring and frictional forces) are too often masked by limitations of the process itself.
For the Down Weight, the technician gradually adds small “gram weights” to the key near its front edge, at the AP. A complete set of gram weights contains weights of several different magnitudes, with plenty of duplicates, so that two or more weights of the same (or different) mass can be stacked onto one another. They are added until the key not only begins to move, but is also able to descend to at least the so-called “let-off” point of the stroke. The keyboard is commonly thumped by hand as each additional weight is added, apparently in an effort to see more of the kinetic friction effect, and less of the static friction (which is always higher than the kinetic). Kinetic friction is in general more consistent, which is likely why this is done. Once the key has descended fully, that particular weight/mass is recorded as the DW, along with the key number. Similarly, the Up Weight is determined by gradually removing weights from a depressed key, thumping the keybed after each removal, until the key is able to return to its top/rest position. The mass value is then recorded as the UW, along with the key number. The Balance Weight is then calculated as the simple average of Down Weight and Up Weight, as mentioned above.
One problem associated with this process, having to do with the sheer tediousness of it, is how accurate the technician can afford to be. If he's just beginning this process for an entire piano, he may start out adding (and removing) very small increments of mass (perhaps 1 gram). By the time he has completed measurements for a third, or half, of the keys, he may resort to adding/removing nothing smaller than 2 or 3 gram weights, simply to make things go quicker. So the answers, already limited by the physics of the process, are further reduced in accuracy by insufficient resolution.
The other limitation of this process—the results not truly representing the desired effects—will now be described. All of the component “static” forces which together are supposed to exclusively determine the DW and UW values can vary significantly as the stroke of a given key action proceeds. The friction occurring at the various joints/interfaces along the keystroke is certainly local in nature, and can vary as the key and action change position. Any spring, whether attached to the wippen or the key or the hammer, will also have its force varied as it is compressed or extended along the stroke. If magnets are at play, they will change distance from each other during the stroke, with corresponding changes in force or torque. And finally, the gravitational forces acting on the hammer (and to a lesser extent other masses in the mechanism) will vary throughout the stroke just based on the trigonometry of the moving levers. The resulting effect of all these components at the AP therefore changes as the key stroke progresses. The Prior Art parameters of DW and UW (and by extension, BW) exist for the sole purpose of trying to quantify these non-inertial effects. The subsequent examples will show how these parameters are in fact deficient in actually measuring that for which they were created. Note that the reasoning is nearly the same no matter which of the “force components” (friction, gravity, springs or magnets) is the culprit. However, since friction would likely behave in a more erratic manner, it will be treated separately.
Once the technician has added enough weight at the AP to cause the key to start moving, the entire key assembly obtains momentum. This momentum, however small it may be, allows the descending key to overcome some or all of the localized “spikes” in friction, thus cruising right through these regions. The more momentum (or speed) it attains, the more friction it can overcome without stopping. Thus any points in the descent where higher friction might be found are effectively masked by the moving key/mass assembly. In the best scenario then, the DW represents the amount of force required to press the key down slowly, at the most resistant point in its downstroke. If only one small portion of the stroke, say near the top, contains this large friction value, the prior art Down Weight nevertheless reacts as though this frictional force is acting over the entire stroke. Perhaps even a more misleading case would exist if the friction near the very top of the stroke was relatively small, becoming larger at points further down the stroke. The prior art value of DW would thus err on the small side. This is because once enough mass is added, the key mechanism would begin moving, thus acquiring momentum. It may very well acquire enough momentum to “cruise” right on through the point(s) of higher friction further in the stroke. The result is obviously a Down Weight that is smaller than it should be, with the “sticky” region having been glossed over entirely.
The upstroke (when calculating Up Weight) has a very similar limitation, as the entire key mechanism (hammer, key, embedded keyleads and applied gram weights) begins acquiring momentum, once enough weight has been removed for ascent to begin. If friction is locally high at the point near let-off where the key stopped when evaluating the Down Weight, then considerable weight must be removed to get the key moving upwards again. And once it starts moving, the friction may decrease quickly for some or all of the remaining upstroke. Yet the Up Weight had to be “artificially” reduced to get beyond the “sticky” region near the bottom. This would lead to an artificially low value for UW. Similarly, if this bottom region happens to have a locally small friction, then less weight must be removed to get the key moving upwards. Then, the key may likely acquire sufficient momentum to “break right through” a “stickier” region closer to the top of the stroke. In this case, the Up Weight value would be artificially high.
So the measurement of DW and UW, and therefore BW and Friction, is severely impaired by the variation of the frictional component along the keystroke. If it just so happened that during the stroke, this friction component (at the AP) remained totally constant as all members moved slowly along, then these equations, and the accompanying method, would be more valid. However, it is much more likely that friction, in any number of joints/interfaces in the action, varies as the key moves along.
The force components of gravity, springs and magnets (if they exist) are also likely to vary with key position. Of course, they will likely vary more smoothly than would friction. This is another way of saying that the TRUE Balance Weight (i.e., the induced upward force at the AP due to gravity/leverage of the entire key mechanism, springs and magnets) will often change across the keystroke. The moment arms of the various levers can change as the stroke ensues. For instance, in a grand piano, the moment of the hammer mass about its shank's pivot usually increases as the key is further depressed, just due to the trigonometry. In an action using magnets, the “assisting” force might also change somewhat as the key descends. Any springs at work would also, by their very nature, impose continuously varying assistance—or impedance—at the AP. For instance the hammer return springs in an upright piano exert less resistance at the AP at the top of the stroke than at the bottom. With current practice, the effect of all these variations can be easily missed for the same reason as varying friction can be missed: acquired momentum of the gram weights and entire key action. Once the gram weights, and indeed the entire key mechanism begin moving, subsequent increases in True BW—due to increases in these forces—can be “cruised through”. As with the friction, this would lead to artificially low measured DW's. In that same scenario, where True BW is higher when the key is depressed than when the key is near its rest position, the measured UW's would be artificially high, since less weight would have to be removed to get the key moving up. As the key ascends, the decreasing upward force (at the AP) due to gravity, springs and magnets may not be able to stop the key before reaching the top. This would result in an artificially high UW.
As will later be seen in the Description section, the current practice of measuring DW and UW is also limited for a slightly different reason. In that section, a rigorous formulation of the friction equation will reveal the following:
Both of these scenarios are closely related to what was already discussed above, simply phrased in a more theoretical manner. In other words, during DW measurement, if the key begins descending, and reaches a nice, constant velocity at, say, 1 mm, and then encounters additional friction at, say, 4 mm, there may be enough acquired momentum to “cruise through” this region, as discussed above. But in practice, what is happening is that there is a deceleration of the gram weights, due to the increased frictional resistance. So even though the momentum may be sufficient to glide through this region without stopping, a deceleration has occurred, which violates the conditions of the governing equations.
Another limitation of the current practice has to do with the “thumping” commonly done after each gram weight is added or removed. This “thumping” of the bottom of the keybed is normally done with the fist or palm of the hand. In essence, it serves to create some small movement of the measured key. An upward thump briefly accelerates all keys in the upward direction. However, the key which already has weights on it will not accelerate upward as much as its neighbors, thus creating some relative movement of that key. This changes the friction from static to kinetic, with the latter being generally smaller. The problem is, this thumping really needs to be fairly consistent in intensity. Otherwise, a gram weight that would otherwise be sufficient to cause key depression can't because its key didn't make the transition from static to kinetic friction. All because the thumping done with that gram weight in place wasn't quite as intense as usual.
Some experiments were reported as having been performed by Clarence Hickman, using some sort of “touch analyzer” in 1929. This work is briefly described in a technical paper entitled “Description of the New Piano Action” (Description of the New Piano Action” by Clarence Hickman, Ampico Research Laboratory, circa 1929, 14 pages), which is believed to have been written by Hickman in 1929, when he worked for Ampico. According to the Ampico paper, the device sat in front of the piano and had a member that contacted the top of the key. The device also had some sort of force transducer apparently. In a 1969 interview with Bardel, Hickman was either unwilling or unable to explain how the force was measured. According to this interview, the contacting member was made to move down against the key by a “hand cranking device”. Hickman managed to create some graphs of the resulting force vs. displacement as he cranked the device to make the key move down and then back up. It is unclear if anything approaching constant speed was achieved, or if Hickman was even striving for that. In both the Ampico paper and the 1969 interview, he was unable or unwilling to explain how the apparent correspondence between force and displacement was obtained in 1929. In the interview, he suggested he tried to “gently” crank the device to complete a cycle. The graphs he made do show a significant force difference between the downstroke curve and the upstroke curve. One such graph is shown in
In the Prior Art, the distance that a key can travel, measured somewhere near the front of the key, is known as the Key Dip. In the Prior Art, this parameter is not so much measured as it is checked when necessary. The two main tools used for this checking are a key dip block or a ‘Jaras leveling and key dip tool’. Both of them are only good for a conditional check of a given key. That is, each tool comes in one “size”, which makes it good for determining when the key dip is that one exact value. So if one uses a ⅜″ key dip block, or a ⅜″ Jaras tool, one can learn if the key dip is greater than, equal to, or less than this ⅜″ value. If you had many tools, all configured for different values of key dip, it might be theoretically possible to determine the exact value of the key dip. But that is highly impractical. In reality, the tools are used as part of the adjusting process, rather than for measuring per se. So, the technician uses a ⅜″ tool if he wants to set the key dip to ⅜″, a 9/16″ tool if he wants to set it to 9/16″, etc. The tools are used in concert with a shimming process underneath the front of the key, adjusting shims until the key dip matches the specification of the tool. Another concern while using the tools is the amount of force to apply to the key for it to be considered in its “fully displaced” position. The standard practice is supposed to be the application of 250 grams (force) to the top of the key. This process is rather tedious work, and takes at least an hour for a typical piano.
Some experiments have been performed in which the top/front region (the “playing region”) of a piano action was set into motion and a reaction force measured. As mentioned above, Clarence Hickman reportedly did this with some sort of mechanical device in 1929. As reported, he used this device on a new piano action design he had recently invented, and also on a traditional design, to demonstrate that his design produced less friction, cranking the device by hand to get the probe to move the key down, and back up again. The device was reported to have rested on a large base in front of the piano. It is unclear from the literature how Hickman was able to measure force, and furthermore how he was able to generate a graph relating force and key displacement. Several of these graphs exist, one of which is shown in
As part of an effort to dynamically model the grand piano action, Brent Gillespie in 1992 authored a paper (“Dynamical Modeling of the Grand Piano Action” by Brent Gillespie, in Proceedings of the International Computer Music Conference, pp. 77-80, 1992) in which the results of his modeling were tested with some laboratory experiments. According to the paper, Gillespie excited the key and observed, through both high-speed video and position encoders on the action mechanism, the movement of various components. A strain gauge was placed between a kevlar driving member, which was coupled to a large motor, and the top of the key. This recorded the interaction forces. The description of the apparatus is not clear in the paper, but it appears to be driven by a traditional motor in an open-loop fashion. Though encoders were used, there is no indication they were used in realtime as a means of controlling the motor output. It appears that they were used only after the fact, to plot out positional data of various elements.
Martin Hirschkorn attempted to improve upon existing mathematical models of the grand piano action, and published a thesis in 2004 at University of Waterloo to this effect. His thesis was entitled “Dynamic Model of a Piano Action Mechanism”. In it, he describes some experiments he performed, in an attempt to verify certain aspects of his derived model. For these experiments, a standard rotary motor was situated in front of the piano key. A 4-inch long aluminum arm was attached to the shaft, converting the small rotation into essentially linear downward motion at the top of the key. A “one key” action model from a grand piano was used. A small “button-type” load cell was adhered to the top of the key, for measuring reaction force. He first did several sample runs using an actual pianist, where the load cell measured the forces between finger and key. Some of the resulting force profiles were then used to painstakingly determine a current input profile for the motor which yielded similar reaction forces at the key. Of course, this was only applicable for that one particular action used in the experiments. The author was very interested in the resulting motion of various components of the action during excitation, so he positioned rotary encoders in three locations on the action, and also recorded other motions with high-speed video.
The invention defines new and improved parameters (Down Force, Up Force, Balance Force, and Average Friction) for evaluating important “stroke characteristics” of individual key actions of one or more pianos or keyboards, and describes exactly how these parameters are to be tested, measured and determined. The new parameters are designed to replace the prior art parameters of Down Weight, Up Weight, Balance Weight and Friction.
The invention further discloses various methods, means and apparatus for accurately testing, measuring and determining these new parameters, with the capability of performing thousands of measurements—on thousands of different key mechanisms—in a short amount of time.
These and other objectives and advantages of the invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings.
While the invention is susceptible of various modifications and alternative constructions, certain illustrated embodiments have been shown in the drawings and will be described below in detail. It should be understood, however, that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the intention is to cover all modifications, alternative constructions, and equivalents falling within the spirit and scope of the invention.
The method proposed herein to overcome the inaccuracies inherent in the prior art parameters of DW, UW, BW and friction is to measure the resisting force continuously as the key is forced to descend in equilibrium (i.e., at constant speed). And also, to measure the contact force continuously as the key is allowed to ascend at constant speed back to its initial position. The damper lever would be fully disengaged for all these measurements. The method would then use the acquired force data to calculate an average contact force for the downstroke, and an average contact force for the upstroke. Downstroke, as used throughout this application, refers to any forced movement of the AP in a downward direction. Upstroke, throughout the application, refers to any movement of the AP in an upward direction. Rigorous formulations of the friction equation, using variations of Newton's 2nd Law, will now be presented. This will allow still more weaknesses in the prior art methodology to become evident. Note that the resulting equation has the exact same form as the age-old friction equation. However, the various terms in the equation will be seen to be so different from their prior art counterparts, that new names will be given them. In order to explain the true formulation of the friction equation, a model will first be created that represents the actual piano key mechanism well.
As seen in
The effect of the hammer shank on the static force at the AP is rather small. For this reason, only half of the shank is represented in this model, the “outer” half—closest to the hammer head. The “inner” half, closest to the pivot, has little effect on the Balance Weight at the AP. In the model, the shank begins at S, and extends all the way to G, the hammer head mass location. Since it represents half of the length of the actual shank, the point S is halfway between P and G. Thus, point S has exactly half of the leverage that point G has. That is, it travels half as fast as point G, since point P is fixed. The mass of the “half-shank”—designated mF—is chosen to be at point F, which is simply half way along the “half-shank”. This position obviously corresponds to the center of mass of the half-shank. So one can see that in this model, the speed of F is exactly 75% of the hammer head speed (point G). This corresponds exactly to the real-world half-shank.
In the model, friction exists at the single pivot, and is of sufficient magnitude to exactly represent the combined effects of friction at the various pins and sliding joints in the true action being modeled. The equivalent effect of this frictional resistance—translated to point A—is denoted by an upward or downward force Ffr, acting at point A. Ffr acts upwardly if the rotation of the model is CW, and downwardly if the rotation is CCW. The force applied at point A in moving point A downwardly is designated Fdn. The reaction force at A, as point A is allowed to move upwardly, is called Fup. All of these force vectors, including those due to the weight of all the separate masses in the model, are applied to the model in
As part (a) of the first method, point A is first accelerated by a force Fdn to some constant downward speed, then maintains that constant tangential speed for some finite distance. During this movement, which is a controlled downstroke, the resulting value of Fdn is continuously measured. Once point A achieves a constant speed, Newton's 2nd Law can be easily applied to the motion to obtain one of the two necessary equations. The end result is an equation for Average Friction, AF. This rigorous formulation of the equation for AF will prove that the method I propose for measuring DW and UW (and therefore friction) is indeed the only method that stays true to all of the assumptions inherent in the formulation.
For part (a), the downstroke, the Work-Energy Theorem will be implemented. I will define “y” as the vertical displacement of point A, with positive direction directed downward. The theorem will be invoked between two points of this downward movement, once constant downward speed has been achieved. The initial point will have y=p, while the final point will have y=q, where q is greater than p. The Work-Energy Theorem states that the final kinetic energy (KE) of some system is equal to its initial KE plus the sum of all work done on the system by external forces between the initial and final states. So the equation starts out as:
KE)p+W)ext=KE)q
Using the force vectors shown in
KE)p+Σi=B→DmigΔhi−Σi=E→GmigΔhi−∫pqFfrdy+∫pqFdndy=KE)q
Because I insisted that the speed of the system be already constant when this integration begins at y=p, and remain constant when y=q, one sees that the two kinetic energy terms are equal, and thus drop out of the equation. That leaves me with:
Σi=B→DmigΔhi−Σi=E→GmigΔhi−∫pqFfrdy+∫pqFdndy=0 (Equ. 1)
The Work-Energy Theorem will also be implemented. Here, point A begins in a more downwardly position, and is allowed to accelerate upwardly to some constant upward speed, then maintains that constant tangential speed for some finite distance. Once this upward constant speed is attained, Newton's 2nd Law can be easily applied to the motion to obtain the second of the two necessary equations. Note that for this movement, the positive direction for y will be considered UP. Also note that the final point of the downstroke movement, called “q” in part (a), will be the initial point of the upstroke movement, and will now be called “p”. The final point for this upstroke will be called “q”, and is the same point as “p” for the downstroke movement. And similar to part (a), assume that point A has already reached a constant speed by the time y=p in this upstroke. And assume that this speed stays constant all the way until y=q. The initial equation is the same as in part (a):
KE)p+W)ext=KE)q
From FIG. 7, this becomes
KE)p−Σi=B→DmigΔhi+Σi=E→GmigΔhi−∫pqFfrdy−∫pqFupdy=KE)q
As in part (a), my assumptions forced the initial and final KE's to be equal, so the equation becomes:
Σi=EΘGmigΔhi−Σi=B→DmigΔhi−∫PqFfrdy−∫pqFupdy=0 (Equ. 2)
Now by adding Equations 1 and 2 to each other, the potential energy terms drop out, and one is left with:
∫pqFdndy−∫pqFupdy=2∫pqFfrdy
Solving this for the friction integral, it becomes:
The above becomes, after dividing both sides by (q−p):
Since the average of any function of y, from y=p to y=q, is defined as the definite integral of that function from p to q, divided by (q−p), one sees that three separate averages appear in this equation. These three will be named as follows:
Given this new nomenclature, Equation (3) above becomes:
So, the Average Friction over a given range of key displacement is equal to half the difference of the Average Down Force and Average Up Force, over that same range. Note that it has the exact same form as the traditional friction equation, with friction, DW, and UW replaced by AF, DF, and UF.
If one wants to formulate the same governing equation, but in the time domain, rather than displacement, the preferred version of Newton's 2nd Law to use would be the Impulse-Momentum equation, or similarly the Angular Impulse-Momentum equation. The latter states that the final momentum of the system must equal the initial momentum plus the summation of all angular impulses imparted to the system. Interestingly, one finds the exact same assumptions necessary in this formulation, as were found in the Work-Energy formulation. Namely, no acceleration or deceleration can occur along the range of calculation. Any such change in velocity would necessitate the addition of impulse terms representing inertia forces/moments. Furthermore, to ensure a fairly simple equation, the initial and final momentums must be the same.
The downstroke is considered first, with the initial state defined as time “a”, with point A relatively high, and the final state defined as time “b”, where point A is relatively lower. Also, point A is already moving down at a constant speed when time “a” is reached. That is, the entire integration is done while point A is moving at a constant downward speed. Looking at
Hb−Ha=∫abMdt
where Hb and Ha are the angular momentums at times b and a of all the particles, and M is the total moment about P due to the external forces on the system, at any given time t. So the integral of M from time “a” to time “b” is therefore the integral of each of these separate external moments, about P, between time “a” and time “b”. Calling the velocity of a given mass “i” in
Since the initial and final speeds were forced to be identical, the LHS of this equation becomes zero, leaving:
Now the same equation is used on the upstroke, integrating from another time “a” to another time “b”, and ensuring that (b−a) in the upstroke equals (b−a) in the downstroke. In addition, the location in the downstroke corresponding to the downstroke's time “b” is the same exact location corresponding to the upstroke's time “a”. And of course, the location in the downstroke corresponding to the downstroke's time “a” is the same exact location corresponding to the upstroke's time “b”. And as before, point A is already moving up at a constant speed when time “a” is reached. That is, the entire integration is done while point A is moving at a constant upward speed. Referring again to
Since the initial and final momentums of all point masses are identical, the lefthand side of this equation becomes zero, leaving:
Now Equ. (7) is subtracted from Equ. (6). All of the gravity-based angular impulse terms drop out, leaving:
0=∫ab(rA×Fdn)dt−∫ab(rA×Fup)dt+∫ab(rA×Ffr)dt|dn−∫ab(rA×Ffr)dt|up
Notice the “dn” and “up” tacked onto the two friction terms, to remind us that one is for the upstroke, and one for the downstroke (the directions of the force vector are opposite). Performing the cross products, and looking closely at the directions of the vectors in
0=∫ab(sin 270°·rA·Fdn)dt−∫ab(sin 270°·rA·Fup)dt+∫ab(sin 90°·rA·Ffr)dt|dn−∫ab(sin 270°·rA·Ffr)dt|up
Bringing all the constant terms out in front of the integrals, and evaluating the sine terms, gives:
∫abFdndt−∫abFupdt=2∫abFfrdt
Dividing through by (b−a) gives:
As mentioned before, the definite integral of any continuous function from a to b, divided by (b−a), is the very definition of the average of that function over that interval. These three “average” equations are:
So, by implementing a different form of Newton's 2nd Law, which keeps things in the time domain, I have revealed three different equations—in terms of “t”, rather than “y”—for the Average Down Force, Average Up Force, and Average Friction. As long as the time range (from a to b) corresponds exactly to the displacement range (p to q) in the corresponding equations of Method 1, then the resulting averages must be identical. Since they are identical, I can use the same terms I introduced earlier to describe them, namely: DF for the average of Fdn, UF for the average of Fup, and AF for the average of Ffr. Putting these three terms into Equ. 8 above, and dividing by 2, gives the result for average friction:
This is exactly the same equation that was derived in Method 1 with the Work-Energy method.
In essence, the rigorous formulations given here, using Newton's 2nd Law in two of its variations, shed light on the important assumptions that are inherent in the final equation for friction, and also in the equations defining DF and UF. The prior art friction equation has been used for many years, with little thought seemingly given to its origin or inherent assumptions. I have made it clear that certain conditions must be met if a good answer is to be the result. And also I have made it clear that the continuous functions of Fdn and Fup must be known, and then integrated, over the range of interest. Simply placing a mass on the key and watching it descend gives little indication of the actual reaction forces occurring as the key descends. The changes in resistance along the descent cause corresponding changes in velocity of the key. Similarly, as the key ascends after sufficient gram weights have been removed, as in the prior art, little is known about the actual reaction force between the weights and the keytop. The changes in resistance as the key ascends cause corresponding changes in velocity of the key. So, not only are the Fdn and Fup functions not known throughout the range, but the important requirement of constant speed is often violated. I have also demonstrated that the Prior Art parameters of DW and UW are also flawed in expressing what they were apparently intended to express: the average reaction force as the key descends slowly or ascends slowly. The most obvious reason for this is the speed of descent or ascent can never be assured to be constant in the Prior Art. If it's not constant, then one simply does not know these reaction forces over the entire stroke, because acceleration terms appear in the governing equations. For all these reasons and more, the embodiments herein provide a much-improved method of measuring “Down Weight” and “Up Weight”, and therefore indirectly friction.
Similar to how BW in the Prior Art is calculated from the simple average of DW and UW, the improved parameter Balance Force (BF) is calculated as the average of DF and UF, as follows:
This represents the combined effect of all non-inertial forces except friction, at the AP. And since it has been demonstrated above that the DF and UF parameters are superior to the DW and UW of the prior art, it will also be true that the new BF parameter is superior to the BW parameter of the prior art. Note also that, because both DF and UF are true averages over the range of interest, it follows from the above equation that BF is also a true average of some theoretical “balance force function” over the range of interest. Just as with their Prior Art counterparts, the region of interest for these new DF and UF measurement should be a portion of the key's stroke prior to so-called “let-off”. This is because let-off brings kinematic discontinuities and extra, unrelated factors into the picture. The friction before let-off has mainly to do with pivot joints and fairly small relative, sliding motion occurring at the capstan and at the knuckle (or butt, if an upright piano). These sources of friction are essentially identical no matter which way the key is traveling—up or down. During let-off, additional friction occurs, much of it only existing on the downward movement of the key. This was expressed graphically in
So for the region of interest (before let-off), the replacement for “Down Weight”, which I have coined Down Force (DF), accurately represents the average force required to depress the key a certain distance, at a constant speed. Similarly, the replacement for “Up Weight”, which I have coined Up Force (UF), accurately expresses the average force acting upwards at the Application Point (AP) while the key is allowed to ascend, with the AP at constant speed, back to its original location. Today, each of the Prior Art values (DW and UW) do not represent a reaction force averaged over all or part of the stroke at all. Rather, they each represent the true reaction force at perhaps only one point—often the top, rest position for DW and somewhere near let-off for UW. DW as measured today typically represents the amount of force required to get the key moving slowly. If the resistance changes after 1 or 2 mm, either from lever arms changing, spring or magnetic forces changing, or friction itself changing, the current method has a good chance of overlooking it. The same logic applies to the current practice of measuring UW, as described before.
An example of the new methods being implemented on an actual piano key action now follows.
Going back to
One can imagine the above “down and up” constant-velocity procedure being performed for any subregion of the stroke, as long as it avoids the let-off area, and as long as the contact is moving at constant speed throughout the subregion, in each direction. Thus you can obtain an average value of DF, UF, and therefore BF and AF, for the key between 1 and 3 mm, or between 4 and 6 mm, etc. The only concern is to make sure that the “lowest” point of the integration (i.e., largest “y”) is not within the start of let-off. In this way, it is now possible to determine if the friction significantly changes along the stroke. If the AF arrived at by integrating between y=1 and y=3 is called AF1-3, and the AF resulting from integration between y=4 and y=6 is called AF4-6, then the two values can be compared. If AF1-3 is significantly less than AF4-6, then it can be assumed that the friction near the top of the stroke is less than the friction closer to the bottom. If the reverse were true, then one knows that the friction at the top of the stroke is greater.
The force data of
It should be noted that the integrations mentioned above, in calculating DF and UF, can be done in any convenient manner. The easiest method, particularly when a computer is involved, is probably to numerically integrate. This method is very easily implemented into readily available computer programming routines, and is the method the present author has chosen to use. Another possibility would be to approximate the entire force vs. time (or force vs. displacement) curve with some best-fit function. This function could be of many forms, including a higher order polynomial. The resulting equation can then be integrated using standard formulas and rules from the calculus. It may be very difficult to get the equation of an approximating function that fits the data nicely, however.
Recall from above that the Key Dip of a key cannot be measured in the prior art, but merely compared to nearby keys, or to some standard, such as a key dip block or Jaras tool. An embodiment of the invention is therefore to allow the Key Dip of any key action to be measured directly. The Key Dip values of all keys on a piano, for instance, can then be plotted and quickly compared to each other. The method is now described. Assuming a means for moving the key action downward, at the AP, in an accurate and controlled manner is available, along with a means for simultaneously measuring the reaction force between the contact and the key top, at the AP, then the following method can be used to determine the stroke, or key dip, of the key action. With the sustain pedal depressed, or damper lever otherwise disengaged, a contact or probe would move the key, at the AP, downwardly at a fairly slow, and nearly constant speed. The contact would continue moving downward until it sensed a sufficiently-prolonged increased resistance, at or above a threshold of force greater than what would be required for achieving let-off and tripping of the jack. This threshold of force should furthermore be small enough not to waste any undue motion compressing the felt, at the front rail between the key and keybed. Once this prolonged increase in reaction force is achieved, the motion of the contact would stop, and its displacement, relative to the “at-rest” position of the key and contact, would be recorded. The value to be used for the force threshold should be at least 250 grams, based on my experiments. As this “keydip evaluation” process occurs, the software control program or routine, as the contact descends against the key, would repeatedly ask the questions:
If the answer to both (a) and (b) is yes, then the net displacement of the AP, at which the threshold force began to be surpassed, is recorded. This value, as measured or confirmed today via current practice means, is known as that key action's “Key Dip”. It usually falls between 9 mm and 10.5 mm for most pianos. Recall that since the AP is following a well-defined displacement versus time, once the time is determined as described in the embodiment, the corresponding displacement is calculated from that relationship. An example of how this key dip measurement process can be implemented, using an actual apparatus, is shown in
Several embodiments described herein relate to a machine for measuring piano action properties by exciting a piano key 73 while simultaneously measuring the resulting reaction forces on the key. One of the main obstacles to be overcome in being able to do this quickly and repeatedly on one key, or many different keys, has to do with addressing the key. That is, before a given run can be made, the contact or probe must know its exact vertical location, with respect to the top of the key being measured. All embodiments of the invention have a motor (61, 61a), a force transducer 67 and a contact 68, the latter corresponding to the exciter or probe. The contact is the portion of the machine that actually touches and moves the piano key, and also transmits the reaction force to the force transducer. The controlled movement and positioning of the contact near or against the key, not including preparatory movements such as Home Address and Key Address discussed below, while simultaneously measuring and recording any reaction forces acting between the contact and the key, is hereinafter referred to as a Run. There can be several runs on one key, each with potentially different movements (constant speed, constant acceleration, downward, downward and upward, etc.), and each designed to extract different information. In all the included embodiments describing a machine, in preparing for the next run, the motor is first brought to its “home position”.
Home position is herein defined to be any one point in the motor's movement that corresponds to some convenient and predetermined vertical position of the contact, relative to the machine itself. So in referring to “home position”, one can be referring to either the motor position or the contact position. In one embodiment, this is the topmost point in the contact's travel. The process of bringing the motor and contact to home position will hereinafter be referred to as Home Address. The Home Address process can purposefully or accidentally result in the contact being either:
(A) well clear of (i.e., above) the top of the key, or
(B) displacing the current key downward by a significant amount.
These two types of Home Address will hereinafter be referred to as Home Address (A) and Home Address (B), respectively. Regardless, Home Address only puts the contact 68 in a known location relative to the machine. Before an actual run is begun, the contact must be exactly located relative to the piano key 73 which is to be the subject of the run. If this doesn't happen, then none of the resulting force data can be accurately known as a function of key displacement. This process of positioning the contact correctly relative to the key will be hereinafter referred to as Key Address. Thus, after the completion of any previous run, or at the start of a series of measurements, the machine first undergoes Home Address, followed by Key Address. Key Address consists of finding the top of the key at its rest position, and stopping the contact at that point, but may also include further positioning of the contact with respect to the key.
If Home Address (A) has just occurred, then the embodiments accomplish key address (the downwardly-moving Key Address process) by:
In steps (1a) and (2a), the method for determining initial contact with the key 73 can vary. The force transducer 67 itself can perform this function. In step (2a), when the contact 68 begins to contact the key, the force sensed by the force transducer will increase sharply, as will its output voltage. This could be easily seen by the user on a Data Display Means. Alternatively, some sort of contact sensor or proximity sensor can be used. A proximity sensor could be built into the contact itself, or could exist nearby the contact 68. It could be of any standard type. These might include capacitive, inductive, infrared, laser-focusing. As long as the design and output of the sensor allows the controlling program (the software operating as specified herein, such as on computer 93 or other cpu-based computing device, discussed below) or user to know exactly where the top of the key is, relative to the contact, it could be used. If a capacitive sensor were used, it could be embedded into the contact itself for example. The sensor head may be situated above the actual contact point by some distance. Calibration could first be done to determine what the sensor's output voltage is when a typical piano key is brought fully into contact with the contact 68. In operation, the output of the sensor could then be connected to another channel of the A/D converter 90. The resulting voltage could easily be displayed on a Data Display Means. So during Key Address, one would then know exactly what voltage value on that channel corresponds to a typical key beginning to touch the contact 68.
The optional step (3) could be useful in certain types of runs. For instance, if one desired a run where the contact needs to be moving at constant speed even early in a downward stroke, then this extra step would be implemented in the Key Address. One could utilize this additional step to accurately position the contact 1 or 2 mm above the key, giving the motor and contact 68 a chance to gently accelerate to a constant speed before contact with the key is made.
If Home Address (B) has occurred, then the embodiments accomplish key address (the upwardly-moving Key Address process) by:
As mentioned above, in the description of the downwardly-moving Key Address process, the force transducer itself can be used to determine the “separation point” in step (2b). As soon as the contact 68 begins to separate from the key 73, the voltage output from the force transducer 67 will reduce to a point near zero. This change in voltage could easily be sensed by the controlling program, or seen on a Data Display Means by the user. And as mentioned above, a proximity sensor could also be used for this purpose. If a capacitive sensor were embedded into the contact itself, for example, then it would output a certain voltage while in direct contact with the key. Once the contact left the key, this voltage would change significantly. This voltage change would be easily detected by the controlling program, or seen on a Data Display Means. Any device, arrangement or means—including the force transducer 67 or the proximity sensor—that generates a signal, or changes its output signal, when the contact 68 either begins touching or begins separating from the key 73, is defined herein as the Key-Rest-Detection Means. In general, Key-Rest-Detection Means is a means for providing a signal indicative of the relative position between the contact 68 and an at-rest key 73. In the embodiments described herein, Key-Rest-Detection Means is a means for providing a signal indicative of a change in contact condition (such as contact initiation or break from contact) between the contact 68 and a key 73. Key-Rest-Detection Means may also be means for providing a signal indicative of some predetermined offset clearance between the contact 68 and an at-rest key 73.
The output signal from the Key-Rest-Detection Means, upon completion of Home Address, may also be used to indicate whether it was Home Address (A) or Home Address (B) that occurred. This could vary from key to key, with very low keys resulting in a Home Address (A) (i.e., the contact 68 being well clear of the key top), and very high keys resulting in Home Address (B), where the contact 68 is displacing the key downward. In the Home Address (A) case, the output from force transducer would be around zero volts, assuming that the bridge was balanced and stable. A capacitive proximity sensor, if utilized, would then register a voltage quite different from its known “direct contact” value. In the Home Address (B) case, the output voltage from the force transducer 67 would be some significant value, since a significant force is now acting on the contact. Similarly, if a capacitive proximity sensor were being used as the Key-Rest-Detection Means, the sensor voltage would then correspond to the known “direct contact” value, obtained from previous calibrations on typical piano keys.
The means used to move the contact 68 substantially vertically per steps (1a) and (1b) of Key Address is hereinafter known as the Contact-Adjusting Means. It can take on various forms, as will be seen below in some of the embodiment descriptions.
One embodiment of the invention is shown in
Referring to
Referring again to
On one vertical face of motor support block 59 are two threaded studs 79 (see
A description of how the various components of the embodiments work together electrically will now be given. The electrical diagram of
Still referring to
Regarding the three transistor relays TR2, TR3 and TR4 near the top-right of
In the apparatus embodiments of the invention such as described and shown, the blade 71 and position sensor 72 could be replaced by an encoder that rotates, or translates, with the motor shaft, depending on the type of motor involved. The encoder would then provide the output signal indicative of the position of the motor. Based on the geometry of the various parts of the embodiments, one could quickly determine the corresponding output signal of some desired “home position”. So during operation (the Home Address process), as soon as the computer 93 sensed that predetermined output signal from the encoder, it would know the motor was at home position and end its movement. In this manner, the encoder would replace the functionality of the blade 71 and position sensor 72.
In general, the pins 2, 4, and 6, which are part of the motor control means, could be external to the computer 93. One embodiment would have the main program still reside on the computer 93, and it would communicate with a separate “black box” that has its own output pins for controlling the motor(s). The “black box” would have its own processor that is programmed with all the necessary code for controlling the motor(s) via the output pins. Whenever motor output shaft movement was required in the main program, control would be given to the processor in the “black box”. The embodiment might also have Pin 3 and Pin 8 reside on this “black box”. This would leave the USB connection as the only means of communication between the computer 93 and the other components. So in that embodiment, the Motor Control Means would include the output pins, along with the microprocessor code in the “black box” that is controlling them. Other embodiments might have the entire controlling program reside in this “black box”, with the data stored there for eventual retrieval by a flash drive or other date storage memory device.
The flowchart of
Some runs, like the Key Dip run just described, can implement the “sampling” of the force signal right into the loop that actually causes movement of the motor output shaft. A data point is taken at every motor step; that is, each time through the loop. But sometimes, one needs the sampling rate to be independent of the motor stepping rate. Many A/D devices have a “scan” mode, where the A/D is “triggered”, after which it samples the input signal at some given frequency. With regards to the apparatus embodiments herein, certain types of runs are best accomplished in this manner. The flowcharts in
As those skilled in the art will readily appreciate, apparatus according to the invention may be implemented in many variations, such as, but not limited to the following described alternate embodiments.
Different embodiments of the invention, very similar to that of
For those embodiments where a second or auxiliary motor is used, such as described above to implement powered vertical translation means, there could be a separate motor driver for the auxiliary motor, with a relay to toggle between the two motor drivers as necessary. The relay would switch the incoming 24V signal between the two drivers, and the motor controlling outputs (pins 2, 4 and 6) would be connected in parallel between the two drivers. Another embodiment would have only one driver, but with a relay on one or more of the motor leads from the driver. So the motor leads would go to both motors in parallel, but one or more of the leads would first go to a Single Pole Double Throw relay, which would send that signal on to whichever motor was required at the time.
A different embodiment would eliminate the cam, and would incorporate a spur or helical gearset to couple the motor shaft rotation with the arm 65. Any other parallel-shaft gearset could also be used, although space limitations could limit the reduction ratio. In general, the relative size of the two gears would be designed so that the torque at the arm axis 69A would be increased, and its rotation speed decreased, relative to the motor shaft. A similar embodiment would utilize a belt drive, with differing pulley sizes to generate the speed reduction. In fact, any sort of rotary-transmissive means could be used in the embodiments of this paragraph. Regarding Key Address, it could be accomplished with the same Vertical-translation means of the embodiments depicted in
Another embodiment of the invention is shown in
A variation on any of the above embodiments that do not use a Vertical-translation means for Key Address would have the contact movement of Key Address performed automatically by the motor control means, as soon as Home Address is finished. In this situation, there would be no need for the “key address” switch(es). The Contact-Adjusting Means would then consist of the motor 61 and the portion of code in the motor control means that increments the motor. A variation of these embodiments would also have the controlling program react to the signal from the Key-Rest-Detection Means during Key Address, thus eliminating the need for the run-activation switch 76. As soon as the controlling program detected, from the Key-Rest-Detection Means signal, that the contact was barely touching the key in its rest position, it would stop the Key Address movement and begin the actual run. So in these embodiments, the Run-Activation Means would simply consist of the relevant code in the controlling program. The Key-Color-Transition Means is identical or very similar in these embodiments to that of the embodiments of
Another embodiment would be identical to that of
The reason these “geared” embodiments can utilize the motor 61 for the required Key Address movement, eliminating the need for the vertical-translation means, is now briefly described. As long as the arm angle, relative to the top of the key 73, stays below some reasonably small value (6 or 7 degrees at least), the resulting tangential displacement “s” at the contact (contact point) is very close to its component in the vertical (or key-normal) direction. So the same motor angle vs. time profile can be used, even if one key sits 2 or 3 mm above the previous key. For this higher key, the arm may begin the run at 4 degrees above horizontal and end at exact horizontal, with some resulting vertical displacement “a”. For the previous key then, the arm may have only started the actual run at 1 degrees above horizontal, and ended it at 3 degrees below horizontal, with a resulting vertical displacement “b”. But for these small angles, “a” is going to be extremely close to “b”, just based on the trigonometry. Moreover, if the angular position of the contact is sensed or measured or reasonably approximated, the small difference between the tangential displacement and vertical component movement of the contact can be calculated and accounted for in the controlling program, if desired.
On the other hand, with the embodiment of
Another embodiment is shown in
Another embodiment is shown in
Another variation of the embodiments of
A variation of the embodiments of
A further embodiment would have a means for automatically sliding the lower support 52 along the rods after each key is measured, putting the contact 68 in the correct “lateral” location for measurement of the next key. This might be done by replacing the two rods 51 with corresponding ball screws (or other linear translating devices), both turned by a third motor. This third motor could be secured to either of the end plates (part of the support structure). This third motor could be coupled to turn the two ball screws directly or indirectly. The lower support 52 would then be threaded for receiving these ball screws, thus ensuring that it slides laterally as the third motor turns. It would also be possible to have only one of the rods 51 replaced by a ball screw (or other linear translation device), with the third motor then turning only one ball screw to move the lower support. In either case, once a given key has been measured by the machine, the controlling program would cause the lower support to automatically slide to the next desired key. This embodiment, when combined with one of the “automatic” contact-adjusting means already described, would allow the keys over large portions of the piano/keyboard to be measured with no operator intervention whatsoever.
All electrical and electronic circuitry and processes contemplated herein may be implemented using convenient functional and operational modules. All methods involving calculations described herein may be carried out via electronic or digital processes using a conventional computer in a conventional manner with all of its conventional components, or a similar cpu-based computing device, via computer-executable instructions, and conventional data manipulation, storage and operations, implemented in the applicable software and programming modules.
For understanding and interpretation of the description of the invention and the claims, except as otherwise noted, certain capitalized terms used herein are defined as follows:
Key Action (also known as Key Mechanism)—all the levers and other components, including the key and the hammer assembly, which convert key movement into hammer head movement; this includes the let-off components, which serve to free the hammer from the other components before the hammer strikes the strings.
Application Point (or A.P.)—a theoretical point on top of the key, usually 10 to 12 mm from the front edge, where gram weights are historically placed, and where the contact of the present invention excites the key.
Grams—In addition to its traditional definition as a unit of mass, it is used here also as a unit of force; the amount of force that gravity exerts at sea-level on a body of a given mass “x” [grams] will also be considered herein as “x” grams of force, or “x” grams-force.
Contact—the portion of the machine that actually touches and moves the keyboard key downwardly and allows the key to move upwardly, while also transmitting the reaction force to the force transducer.
Run—The controlled movement and positioning of the contact near or against the key, not including preparatory movements such as Home Address and Key Address, while simultaneously measuring and recording any reaction forces acting between the contact and the key.
Home Position—any one point in the motor's movement that corresponds to some convenient and predetermined vertical position of the contact, relative to the machine itself. In referring to “home position” herein, one can be referring to either the motor position or the contact position.
Home Address—The process of bringing the motor and contact to Home Position.
Key Address—The process of positioning the contact correctly, in the substantially vertical direction, relative to the “at rest” key, in preparation for a Run. The means used to do this is the Contact-Adjusting Means.
Controlling Program—code which reacts to various inputs (switches closing or opening, data from A/D channels), makes decisions based on these inputs (like starting/stopping motors and initiating A/D sampling), reads in time files and displacement files, moves the motor(s) accurately, and activates various PO's.
Key-Rest Detection Means—Any device, arrangement or means—including the force transducer or a proximity sensor—that generates a signal, or changes its output signal, when the contact either begins touching, begins separating from, or achieves a certain offset from the key. In other words, a means for providing a signal indicative of the relative position between the contact 68 and an at-rest key 73. The signal from the Key-Rest-Detection Means, upon completion of Home Address, may also be used to indicate whether the contact is clear of, or displacing, the key.
Contact-Adjusting Means—the means used to move the contact as part of Key Address.
Arm—a member that includes a contact and a force transducer, and is coupled to a motor. It will normally rotate about some axis, but can also translate with little or no rotation. It can be driven in a variety of ways by the motor, including through a cam/follower arrangement. Its main purpose is to transfer movement of a driver (motor, cam, gear set, etc.) into approximately-vertical movement of the contact.
Follower—a portion of the Arm whose main purpose is to provide rigid support for the force transducer and/or the contact. It rotates with the arm, and may also be driven by the motor via a cam.
Vertical-Translation Means—a specific type of Contact-Adjusting Means, wherein the arm is not rotated to achieve vertical movement of the contact, nor is the main motor (61, 61a) pulsed or otherwise activated.
Run-Activation Means—software and/or hardware that causes initiation of a Run, upon successful completion of Key Address.
Key-Color-Transition Means—a means for quickly changing the vertical location and/or fore/aft location of the contact 68 in preparation for addressing the keys of the opposite color
Motor Control Means—the software and hardware which provide the signals, necessary for motor output shaft positioning, to the motor or motor/driver combination. It's software is part of the Controlling Program.
Auxiliary Motor—a motor used with a Vertical-Translation Means to move the contact up or down during Key Address without the disturbance associated with turning a knob.—in lieu of a knob—to move the contact up or down during Key Address.
Auxiliary Switch—a switch that is pressed to increment the Auxiliary Motor during Key Address.
Key Address Switch—a switch that is pressed to increment the main motor for performing Key Address, when no Vertical-Translation Means is available.
Time File—a file read in by the controlling program, each line representing the time associated with the corresponding motor step, in order to generate some predetermined Contact Displacement vs. Time curve.
Data Display Means—any means used for producing an output indicative of, or related to, any input or output signal, measured data, analytical results, or operational parameters involved in the apparatus and methods of the invention described herein. It may consist of the display screen of the computer, the audio speaker system of the computer, or a separate device that produces appropriate visual or audible outputs. One of its main functions is to produce, during Key Address, one or more from the group of: (i) visible numbers, which are based directly on the signal from the Key-Rest-Detection Means, (ii) visible symbols, shapes or colors, whose existence and nature is based directly on the signal from the Key-Rest-Detection Means, and (iii) an audible signal, whose presence and nature is based directly on the signal from the Key-Rest-Detection Means.
This application claims priority to US Provisional Patent Application Ser. No. 61/035,438, filed Mar. 11, 2008.
Number | Name | Date | Kind |
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20090282962 | Jones et al. | Nov 2009 | A1 |
Number | Date | Country | |
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61035438 | Mar 2008 | US |