Kinematic Analysis and Synthesis - Mellinger

At first glance, the quick-return, dual slider mechanism does not look complicated, but it can produce output motions equivalent to 5 and 6 bar mechanisms of similar form, as this analysis will demonstrate. The output slider, located in the slot at the top of mechanism, is the most unique part of the design. This slider can translate across the length of L3 and across the slot. The input comes through another crank slider device that translates across L3. The dual sliders produce a quick return effect – the output slider progresses slowly with greater force in one direction and reverses quickly with lesser force in the other direction. When slicing, the cheese grating teeth push into the cheese and progress slowly with great force. Once the slice stroke is complete the grater slides back quickly and the next slice can begin.

Two vector loops were created to describe the position of the mechanism. Using the time derivative of the vector loop equations the link velocities for each point of interest were calculated. The accelerations of the points can also be found by taking the time derivative of the velocity vector loop, and the Coriolis Acceleration of the output sliding joint was highlighted.

An animation of the simulation was created which shows the mechanism operating as well as the Coriolis acceleration acting on the sliders.

Each term was solved analytically in MATLAB and the motion of the mechanism was simulated by varying the input angle with a constant input velocity of 1 rad/s. The following figures show the results of the simulation and highlight the position, velocity, and acceleration of all links and sliders. The mechanical advantage for the input and output bars are also shown.

The output slider relative motion can be observed in the second subplot above. The slider progress from its starting point, 2 inches from the center axis to its extreme position, -2 inches from the center axis, at 200 degrees, but the slider returns to its initial position at 330 degrees demonstrating the quick return effect.

The velocity of the intermediary bar and slider are shown above. The third subplot shows the velocity of the sliders in the axis along link 3.

The Coriolis acceleration can be observed for the input and output slider. As the sliders translate up across the links they also rotate at a rate consistent to the Coriolis acceleration.

The mechanical advantage increases when the slider is nearing the end of its stroke. There is a vertical asymptote because the output bar has no velocity while the input bar has a constant velocity of 1 rad/s.