Assembly Modes of General Planar 3-RPR Parallel Mechanisms when Using the Linear Actuators’ Orientations

In this paper, we show that the number of possible assembly modes for the general planar 3-RPR parallel mechanism, where P denotes active prismatic joints and R denotes passive revolute joints, can be significantly reduced when using the linear actuators’ orientations in-stead of their lengths. The linear actuators’ lengths lead to a univariate polynomial which can have up to six different solutions and thus provides up to six assembly modes. By measuring the orientations of the linear actuators, provided, e. g., by inertial measurement units, only two assembly modes exist. Furthermore, by using two orientations of the linear actuators in addition to the moveable manipulator platform’s orientation, only one assembly mode remains.