I believe that I understand the point that SCIYER is making. The smoothness of the device is a function of the rate of change of acceleration, which is critical with components and systems that have significant issues with resonant behaviour such as spring driven cam followers or relatively "soft" mechanisms where the sudden changes in rate of acceleration may make it difficult for the parts to move smoothly. For example, a cam follower following a simple round cam profile is required to change rate of acceleration very rapidly at the apex of the cam. As the follower approaches the tip of the lobe, the acceleration required to follow the cam will continue to increase and rate of change increase up to the lobe tip, then immediately the rate of acceleration change will reverse, becoming the maximum rate of change reducing acceleration diminishing until approximately mid stroke. This sudden rate of change in loading can cause inertial behaviours in the individual components that may make some systems operate poorly, especially when there are significant differences in stiffness in parts - an example could be when a cam follower floats on the cam because the spring is unable to react at the right time to supply the additional displacement to change the acceleration. This is an issue of the time for parts and assemblies to change the strained shape when accelerations are applied. Think of stopping your car: you can apply the brakes abruptly to stop (rapid change in acceleration) but this will upset the chassis. Conversly you can apply the brakes smoothly, to a higher acceleration without upsetting the chassis to accomplish the same deceleration. At the point when you stop the acceleration drops to zero nearly instantly, causing the car to lurch and bounce on the springs unless you change the acceleration nearing the stop to permit parts to unload the stored strain energy (and some potential energy) with the last few inches of travel having a relatively slow change of acceleration to zero to avoid a jerk. The more smoothly the acceleration transitions the smoother the stop will be. That being said, in this case the parts can be made adequately stiff to avoid issues with resonant behaviour at the low rpm at which he wishes to operate. I am assuming appropriately stiff materials will be used. Now if a flywheel or load were installed on the end of the output shaft opposite the pinion and the shaft was relatively long and slender (low spring rate) the system could start to behave badly at a relatively low rpm as the wind-up in the shaft overtakes the crank when it rebounds as the acceleration is reduced just after the end of the stroke. So I will amend my comment: without more information about details of the design, it appears that it can be made to operate using appropriately stiff materials of adequate cross section. It will be important to keep the mass of the rack reasonably low, and have an adequately stiff guide frame and roller system. The connecting rod will have to be adequately stiff, and the mounting between the motor/crankshaft and the rack frame stiff enough to avoid resonance in the operating frequencies. It will be important to have some flywheel weight in the crank to avoid resonance in the operating range. The output shaft assembly (including whatever load is applied) will have to be adequately stiff to avoid resonant behaviour. Failure to keep the system adequately stiff to prevent operation at resonant frequencies could result in instantaneous loads substantially higher than predicted by the pure harmonic accelerations.
