The Importance of Jerk in Motion Design for Machines

By Dr Kevin J Stamp














Motion designers direct the intended sequence of movements of parts in machines. As you would expect, machine parts always respond to the proposed motion. The response nominally has two components: the steady state and the transient. Usually the transient is obvious as a 'residual vibration' after an index, for instance. Nevertheless, all mechanisms vibrate during and after a motion, even if not observable. The amplitude of vibration principally determines the machine's OEE, speed, lifespan, maintenance schedule, cost, etc.

The machine's reaction to a motion depends on the motion designed for it. If the motion response is poor, efforts are commonly made to reconfigure the parts instead of redesign the motion. Redesigning parts is often expensive and can put schedules back. With servos, redesigning the motion is free and can be done right away.

Let's envisage the machine part is your head, blind-folded and in a helmet! Your head is being interviewed for an astronaut's job. You are in a chair, without a head-rest, in a centrifuge, spinning at with a steady velocity. Your head is being flung outwards with a constant force. You will know must strain to keep your head upright at a continual position relative to your shoulders.

Now imagine a machine component. It is bolted to the chair and cantilevered over the top of the chair's back-rest; it deflects to a consistent position. Nevertheless, as long as the machine component is sufficiently strong enough to 'take the strain ', it will typically be powerful enough forever.

Packing machines have parts that can move back and forth, mixed in with dwell periods. Therefore, machine parts are subject to varying acceleration, not continual acceleration. Varying acceleration means we've got to study at Jerk. Jerk is therate-of-change of acceleration.

Let's say the centrifuge is speeding up. Think of the increase in radial acceleration, and ignore the tangential acceleration. The muscles in your neck are in the procedure of 'exerting themselves more' to keep your head in one place. They're experiencing 'Jerk'. Your neck muscles 'feel ' the rate of change of acceleration as they will be able to 'feel ' how fast the muscles must stiffen.

A mechanical component will repeatedly change its deflection proportionally to the acceleration it is the subject of. Won't it? Yes and No! Yes: if the jerk is 'low'. And no: if the jerk is 'high'.

What's 'low' and 'high'? Let's imagine the acceleration changes from 'Level One' to a 'Level Two'. Level Two might be larger or less than Level One. If the acceleration is modified from Level 1 to Two at a 'low rate', the deflection of the element will 'more or less' be proportional to the immediate acceleration. If it is a 'high rate', the deflection of the component will first 'lag', then 'catch up' and, if there's little damping, 'overshoot' and then repeat. This is both during and after the acceleration transition from Level One to 2. Complicated?

It is less complicated to consider the speediest possible rate of change of acceleration - infinite jerk. This is a step-change in acceleration. It can be any step size, but jerk is always infinite.

Nothing with inertia can make a response to an acceleration that is designed to change in zero time. The deflection of all parts will first lag and then overshoot. They will vibrate. How much?

Try this experiment. Take a steel ruler - one that will simply flex, but not too much. Clamp it, or hold it on the side of a table so it overhangs the table. Suspend a mass above the end of the ruler from zero height - that is, the mass is just touching the ruler. Let go of the mass. You will notice the ruler deflects and vibrates. It will deflect up to two times the deflection of the 'steady-state ' deflection. The ruler wasn't hit, because the mass was at first touching the ruler. The ruler was only subject to a step change in force - equivalent to a step-change in acceleration. The same will happen if you slide the mass . Nevertheless because the total mass is now less, it will vibrate less.

Surely, no one would try to use a step-change in acceleration to a mechanical system if they knew it would vibrate? Well, you might be surprised.

Getting back to your neck; playground rides control jerk extremely closely. Otherwise the designers would be subject to court actions not to the motion.

Therefore a bit about Jerk - the significant motion design parameter that significantly influences vibration of machine parts. The motion design software in-built to MechDesigner allows you to edit Jerk values to any particular value you want.




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