A small twodimensional polar robot with two link variables r

A small two-dimensional polar robot with two link variables, r (the radius) and theta (the angle) is used to perform a straight cut on a 10 inch times 10 inch square plate from the origin (0, 0) to the far comer of the plate (10, 10). The cutting time desired is 10 seconds. Write the forward kinematic (trajectory) equations for x(t) and y(t), where t is in seconds. Write the inverse kinematic equations for r(t) and theta (t) again where t is in seconds.

Solution

1) Here the cut is from one corner to the other along a straight line.

Initial Point = (0,0)

Final Point = (10,10) . So the equation of the line must be y(t) = x(t) or y =x