Indirect Optimal Traj ectory Planning of Parallel Four-bar mechanism in point t0 point m0ti0n

This paper is concerned with trajectory planning of the four-bar mechanism, based on indirect solution of optimal control problem. First, analyzing on kinematics and dynamics of the mechanism is carried out. Then the Hamiltonian function is formed and the necessary conditions for optimality are derived from the theorem of calculus of variations. The obtained equations establish a two point boundary value problem which can be solved with bvp4c command in MATLAB. The derived dynamic equation is validated through Simmechanic toolbox in MATLAB, and then additional simulations are done for trajectory planning of a four-bar mechanism to demonstrate the effectiveness of proposed approach.