Pedal Assist - An Enabling Piano Device

Summary

The goal of this project was to create a portable device that would allow a paraplegic to depress and hold the sustain piano pedal at will, with a budget of $250.

Outcome

The finished device operates by receiving electrical input from the user's jaw flexion, which activates a motor-driven cam and follower mechanism to depress the piano pedal. Additionally, the device's RPM and bite sensitivity can be adjusted by the user.

Details (Excessive details, really. Too fun to not share!)

Problem

This project was such an interesting kinematic challenge. Initially, I thought it would be easy. How hard could it be to move an actuator down an inch?

Au contraire, mon frère.

It takes quite a bit of force to depress the pedal, way more than I thought, and it needs to be done in about a tenth of a second! The device also needed to be quiet and portable, adding more layers of complexity. Although I designed a few different possible solutions, I'll only bore you with the final design.

Eccentric Cam & Follower

Since powerful linear actuators are very expensive (often thousands of dollars), I decided to go with a cam and follower mechanism driven by a DC motor. With that decided, I then worked on answering perhaps my favorite engineering challenge I've solved: what is the torque requirement for this setup? To do this, I needed to understand two things:

1) The resistance of the piano pedal

The only way that I could figure out the piano pedal's resistance was to steal some weights from the university gym (that I, uh, go to very frequently) and put them on the pedal to gauge how much force they took to activate. I tested multiple pianos, and the force it generally took was ~10 lbs. As I'll show later, I opted to model two different scenarios: a constant resistance of 10 lbs, and a spring value of 10 lbs/inch.

2) The mechanical advantage/disadvantage of the cam & follower

This was the fun part. After playing around for a bit, here's some equations I derived:

Where

E = Eccentricity
R_E = Vertical distance from eccentric center to bottom of cam
R = True circular radius
r = Follower bearing radius
h = Moment arm of the pedal's vertical force
x = Linear displacement of follower
ω = Angular velocity of cam
v = Linear velocity of follower
θ = Angle measured clockwise from vertical y-axis
t = time

I was very pleased to find, after learning some more about kinematic geometry, that the linear displacement of the follower (x) is defined by the equation of a cycloid curve. Being an eccentric circle, it shouldn't come at any surprise at all—but I thought it was so cool to find the shape that solves the brachistochrone problem (learn all about this fascinating concept on my blog here).

The most important part of these equations was figuring out where h, the moment arm of the pedal's force, was located and how it varies as a function of θ. At first thought that is was simply Esin(θ), but because the follower is not always directly underneath the true center of the cam, some more trig had to be done to find it. Either way, the maximum moment arm is simply the eccentricity, E, but I wasn't satisfied with just the maximum and wanted a complete prediction of all torque values.

Below on the left is a chart of the torque vs angle modeled in two different force scenarios: 1) the piano pedal acts like a spring with a coefficient of 10 lbs/in and 2) the pedal gives a constant resistance of 10 lbs. Next to it is a torque vs speed chart of the motor that I selected, showing rated and peak torque values. I converted all of my values to metric for ease of comparison with the motor data. Below the two charts is the full table of data for those interested.

V4 Calcs & Data

As one can clearly see, my motor can perform what I need it to do, but it probably shouldn't do it repetitively. However, his motor was the only option I could find that could do what I wanted it to and keep me within budget. In hindsight, I think I should have come up with a clever solution to get around this (like increasing the weight of the follower) but I also didn't want to delay this project for too long.

For the bite sensor, I bought a thin piezo-electric force sensor from Amazon and placed it in a basic silicon mold that I designed. After connecting it to Arduino, I was pleased to find that it was very sensitive to little pressures and worked very well.

More details of this project coming soon!

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