The control of the motion of a pantograph

This work deals with the modelling and control of the motion of a constrained multibody system which is a flexible version of a pantograph. The system is composed of four uniform links, two torque actuated joints and three passive joints. All the links are moving in the horizontal plane, see Figure 1. In the case of a pantograph, the joint pB is attached to the point p4. See [1] for the description and equations of motion of a pantograph. Given two configurations A and B of the system, and a time interval [0,tf]. The problem dealt with in this work is to compute the control torques for each of the actuated joints such that the system will move during [0, tf] from configuration A to configuration B subject to various constraints on the motion.