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.
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