A Method for Solving Dynamic Equations of a 3-PRR Parallel Robot S. Nader Nabavi 1,a , Alireza Akbarzadeh 2,b , Saeed Abolghasemi 3,c 1,2,3 Center of Excellence on Soft Computing and Intelligent Information Processing, Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran a,b,c ali_akbarzadeh_t@yahoo.com Keywords: Parallel Robot, Dynamics, Differential Algebraic Equation. Abstract. 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. Introduction Among advantages of parallel robots over its serial counterparts are improved accuracy, higher stiffness and higher load to weight ratio. The main weakness of these robots is limited and more complex kinematics analysis which can lead to challenges in robot's path control. To control the robot, it is necessary to have an appropriate dynamic model. A number of researchers have controlled robot by using neural networks and without considering the robot dynamics [1]. The inverse dynamics method [2] is used to control the path of a parallel robot with translational motion. Numerical solution may also be used to solve the robot dynamics equations. Although numerical solutions may be sufficient to investigate robot dynamic behavior, it cannot be used directly to control the robot. Therefore attempts have been made to find an analytical solution. One of the problems in formulating parallel robots dynamic is that the number of generalized coordinates is larger than system’s degrees of freedom. This leads to differential algebraic equations (DAE) that is in fact a combination of differential equations and algebraic equations due to dependence between generalized coordinates. One way to solve these equations is to use numerical methods which may lead to instability [3]. Staicu [4] solved inverse dynamics problem of a 3-PRR parallel robot by using virtual work method. Kordjazi and Akbarzadeh [5] investigated inverse dynamics of a triangle 3PRR parallel manipulator using natural orthogonal complement. Robot path control also requires the solution to its kinematics. Kamali and Akbarzadeh [6] presented a method for a general solution to the direct kinematics problem of parallel manipulators in trajectory following by introducing a new concept based on basic regions. Also, Enferadi and Akbarzadeh [7] presented a novel approach for forward position analysis of a double-triangle spherical parallel manipulator. Kinematics and Dynamics model of the 3-PRR Parallel Robot Kinematics Model. The 3-PRR robot is comprised of three closed kinematic chains. See Fig. 1. Each kinematic chain consists of one prismatic joint and two successive revolute joints. The direction of the three Prismatic joints are star-shaped with 120 degrees angle. Additionally, the end- effector is in form of an equilateral triangle connected by three revolute joints. © (2012) Trans Tech Publications, Switzerland Applied Mechanics and Materials Vol. 232 (2012) pp 414-418 doi:10.4028/www.scientific.net/AMM.232. 414