CGA-based novel modeling method for solving the forward displacement analysis of 3-RPR planar parallel mechanism

Abstract

This paper put forward a new geometric modeling method for forward displacement analysis of 3-RPR planar parallel mechanisms (PPMs) under the conformal geometric algebra (CGA) framework. A geometric constraint relationship of four lines intersecting at a point is first given. Then, a new coordinate-invariant geometric constraint equation of 3-RPR PPMs is elaborated via CGA operation. Next, an univariate polynomial equation without algebraic elimination is published. At last, the coordinates of three points on the mobile platform are figured out. The best part of this research is that a complete geometric modeling method by geometric constraint relationship of four lines intersecting at a point is formulated under the CGA framework, which has good intuition and offers a novel idea for solving the other complex mechanisms. Three numerical examples are utilized to confirm the effectiveness of the proposed method.