Question 16.3: Slider-Crank Linkage Driven by a Servomotor to Perform a For...
Slider-Crank Linkage Driven by a Servomotor to Perform a Forming Operation
Given: A slider-crank linkage mechanism (Figure 16-11) has been designed to provide the geometry for a suitable motion of a die in a forming press. The required motion begins from a dwell and moves the slider through a 2-in stroke ending at TDC with crank angle \theta_{2}=0 . The die needs to be brought to zero velocity for an instant at 1.588-in stroke then advanced into the material. It is then pulled back to dwell at 1.400 in before returning to zero. The slider motion timing diagram is shown in Figure 16-11. Rather than design a custom cam to provide the motion and dwells to the linkage crank, it is desired to use a servomotor directly driving the input link of the crank-slider mechanism through a gearbox to obtain the necessary motions and dwells. Machine speed is 120 cycles per min or 2 Hz.
Find: The motion function needed to program a servomotor to drive a crank-slider linkage that provides the required linkage output motion program as defined at the slider.
Assume: The position and velocity accuracy required at intermediate points in the stroke requires that the motion function be applied to the slider and mathematically transformed to a function at the servo axis that accounts for linkage geometry.
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