Abstract: The primary goal is the kinematic and dynamic analysis of a spatial 3 degree-of-freedom parallel manipulator (a 3-RRS parallel manipulator). The architecture of the mechanism is comprised of a moving platform attached to a fixed platform through three identical revolute-revolute-spherical jointed serial linkages. A complete description of the position and orientation of the moving platform with respect to the reference frame requires six variables, i.e., the three Cartesian coordinates of a reference point on the moving platform and three angles. However, since the parallel manipulator has two degrees of orientation freedom and one degree of translatory freedom, which implies that only three variables can be specified independently. Firstly, the constraint equations describing the inter-relationship between the six motion coordinates of the moving platform are derived. Closed form solutions to the constraint equations are found which provide the constrained variables as functions of the unconstrained (specified) variables. Some significant conclusions are drawn from the closed form solutions. Then, the dynamic equations of the parallel manipulator are presented on the basis of Lagrange equation. Based on the dynamic model, the angular velocities, the driving force or torque and consumed energy of the actuators are analyzed through an example. The analysis provides necessary information for dynamic performance analysis, optimal design and control of the parallel mechanism.

Key words: Dynamics, Kinematics, Lagrange equation, Parallel manipulator, Position and orientation