Dynamics Formulation of a Three-Degree of Freedom Parallel Manipulator

In this paper, dynamics equations of a ۳-RRR spherical parallel manipulator are presented using the Lagrangian formulation, and a compact closed-form dynamics model is provided. The dynamics equations are explicitly derived from Lagrange formulation, whereas, in other methods, such as Newton-Euler or virtual work, usually a recursive form of the dynamic equations is obtained. This explicit form of the equations is very convenient for applying various control schemes. To this end, linear and angular velocities of robot components are expressed in some recursive matrix relations with respect to reference frame as functions of selected generalized coordinates. Describing the reference position and rotation motion of the mobile platform, the inverse dynamics problem is developed. The results are used for verification of the presented dynamics model, as will discussed based on obtained simulation results, while a prototype has been manufactured for experimental studies.

Keywords:

Spherical parallel manipulators , Lagrangian formulation , closed-form dynamics , inverse dynamic problem