Question

Problem 3: The figure shows the sketch of a 2 degree-of-freedom (planar) robot arm, where the link 1 (i.e., the yellow link) and the link 2 (i.e., the pink link) are attached through a prismatic (sliding) joint which only allows for a relative translation. The joint O is equipped with a motor that supplies the external torque, t(t), whereas the joint A is equipped with a pneumatic actuator that supplies the external force, F(t). Mass centers of the links 1 and 2 are marked by the points C and C2, respectively. Note that a fixed right angle is formed between the link axes as marked in the figure. Neglecting joint frictions, and taking e(t) and s(t) as generalized coordinates, determine: a) The total kinetic energy of the system. b) The total potential energy of the system. c) The total non-conservative work expression. d) Equations of motion of the system, using Lagrange's technique. (Show all your work - Do NOT express the system equations in matrix form) s(t) ---- --------- 6.2 90° m2 m , ----------