(Solved): iv. Consider that the typical cyclic motion that the workpiece is to make is defined by a trapezoid ...

iv. Consider that the typical cyclic motion that the workpiece is to make is defined by a trapezoidal velocity profile. The load is to be moved a distance of $$1.0$$ in in $$300\mathrm{ms}$$, wait there for $$200\mathrm{ms}$$ and then move in the reverse direction. This motion is repeated continuously. Assume the $$300\mathrm{ms}$$ motion time is equally divided between acceleration, run, and deceleration times, $$t_{\mathrm{a}}=t_{\mathrm{r}}=t_{\mathrm{d}}=100\mathrm{ms}$$. a. Calculate the necessary torque (maximum and continuous rated) and maximum speed required at the motor shaft. Select an appropriate servo motor for this application. b. If an incremental position encoder is used on the motor shaft for control purposes, what is the required minimum resolution in order to provide a tool positioning accuracy of $$40?\mathrm{in}$$.