A Method for Solving Dynamic Equations of a 3-PRR Parallel Robot
In this paper, kinematic relationships for a 3-PRR planar parallel robot are first presented. The robot dynamics equations are formulated using Lagrange equations of first kind. The derived equations are a mixed set of differential and algebraic constraint equations, DAE, which must be satisfied simultaneously. In order to solve the robot dynamic equations, a new method is presented in which the dynamics equation is first partitioned into two parts. The constraint equations and the dependent coordinates are next eliminated. This reduces the dynamic equations to a set of differential equations as a function of three independent coordinates. Finally, a trajectory for the robot end-effector is specified and PD controller which follows the desired trajectory is implemented. The proposed method significantly simplifies the solution of the dynamics equations.
S. N. Nabavi et al., "A Method for Solving Dynamic Equations of a 3-PRR Parallel Robot", Applied Mechanics and Materials, Vol. 232, pp. 414-418, 2012