A passive tuned mass damper for hand tremor

This was a solo midterm with six required deliverables. Kian was the only contributor to the design and the prototype build.

The MATLAB dynamic model and the background research sat alongside these as supporting work. All three source documents are downloadable at the bottom of this page.

The device is meant to be worn whenever tremor gets in the way of something that needs a steady hand, which in practice means cooking, writing, shaking hands, holding someone. That framing set the constraint: it has to be light, self-applied, and worn in public without drawing attention.

The biomechanical model treats the lower arm as a beam pinned at the elbow, driven by bicep and tricep forces, with the forearm and hand masses distributed along it. Tremor enters the model as involuntary activation of those same two muscles rather than as an external disturbance.

One simplification carries the whole analysis: gravity drops out. The postural muscles are already active and already cancelling gravity, so the only forces left unbalanced are the ones the twitch adds. The device hangs off the arm rather than off the ground, so it cannot counter gravity and does not need to.

The first concept braced the upper arm to the wrist with a passive piston, adding stability by resisting motion across the elbow. It was modeled in Creo and then discarded: bulky, heavy, awkward to put on alone, and it fought the elbow rather than the tremor.

The replacement stays entirely on the forearm and stops resisting motion altogether. Instead of bracing the joint, two spring-mounted masses are tuned to oscillate out of phase with the tremor, so the weight stays roughly where it was when a twitch fires and the reaction damps the arm. Small, light, and something a patient can put on without help.

A static model was never going to work for this, since the device only does anything while moving. Everything downstream had to be dynamic.

Tremor is modeled as a sinusoid, F_tremor = A sin(ωt), which the literature supports as a working approximation of postural tremor. The damper is a classic tuned mass damper, the same device used to stabilize tall buildings, scaled to a forearm.

Two coupled systems get written out: the arm, carrying the tremor force, and the damper mass riding on its spring and dashpot. The coupling terms are the relative displacement and velocity between them, c_d(ẋ_d − ẋ_p) for damping and k_d(x_d − x_p) for the spring. Assuming steady-state harmonic motion and substituting complex exponentials reduces the pair to a solvable expression for the damper force.

Tuning is the whole game. For maximum suppression the damper’s natural frequency has to match the tremor frequency, ω_d = √(k_d/m_d) = ω_t, which fixes the mass once the spring rate is chosen. That relationship is what sets the weights in the prototype.

Rather than hand-solve for a single tuned frequency, the four-state system was integrated numerically in MATLAB with ode45, tracking hand position, hand velocity, damper position, and damper velocity over a 60-second run.

The forcing function is deliberately messy, because real tremor is. It runs at a 5.5 Hz base frequency with a ±2 Hz sinusoidal drift and half a hertz of random noise on top, and the amplitude envelope varies smoothly up to 5 mm with a 30 percent chance of dropping to zero at any moment. That last detail matters: a damper tuned to a perfectly steady sinusoid is an easy problem, and tremor does not behave that way.

System parameters came from anthropometric data, a 1.2 kg forearm and 0.4 kg hand against a 0.05 kg damper mass at 20 N/m and 5 Ns/m. The output plots hand displacement with and without the device on the same axes, alongside the damper’s own response, so the phase relationship is visible directly.

The Creo assembly is the intended build: two damper housings holding sprung lead masses, joined by arms to a circular center support that sits on top of the forearm. Box, spring, and arm dimensions were sized against anthropometric tables using a 77 in frame, giving a 0.95 in spring height inside 1.9 in of travel.

The physical prototype is deliberately low fidelity, built in five hours from 1/8 in foamboard, hot glue, a compression shirt sleeve, and 150 g of split shot. Two sleeves were built, left and right, at 50 g and 25 g per box, so the effect of damper mass could be felt rather than only simulated. The risers are asymmetric, three on one side and four on the other, so the arm assembly sits level once the offset boxes are mounted.

Next iteration: metal or plastic housings in place of foamboard, real springs carrying the masses instead of glued-down weights, and an adjustable strap system rather than a cut shirt sleeve.