Geometric approach for kinematic analysis of a class of 2-DOF rotational parallel manipulators

Euler angles are commonly used as the orientation representation of most two degrees of freedom (2-DOF) rotational parallel mechanisms (RPMs), as a result, the coupling of two angle parameters leads to complexity of kinematic model of this family of mechanisms. While a simple analytical kinematic model with respect to those parameters representing the geometrical characteristics of the mechanism, is very helpful to improve the performance of RPMs. In this paper, a new geometric kinematic modeling approach based on the concept of instantaneous single-rotation-angle is proposed and used for the 2-DOF RPMs with symmetry in a homo-kinetic plane. To authors' knowledge, this is a new contribution to parallel mechanisms. By means of this method, the forwards kinematics of 2-DOF RPMs is derived in a simple way, and three cases i.e. 4-4R mechanism (Omni-wrist III), spherical five-bar one, and 3-RSR&1-SS one demonstrate the validity of the proposed geometric method. In addition, a novel 2-DOF RPM architecture with virtual center-of-motion is presented by aid of the same method. The result provides a useful tool for simplifying the model and extending the application of the RPMs.