On the coupler curve of 3R2C linkages

The purpose of this paper is to investigate the properties of the coupler c urves generated by all 3R2C linkages. First, the 3x3 matrix with dual eleme nts is used to derive the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are f ound by the D-H matrix. Finally, homogeneous coordinate is introduced to th ose displacement equations, and the order and some critical properties of t he coupler curve are investigated based on the theories of algebraic curve and analytical geometry of three dimensions. In addition, RCRCR and RRCCR l inkages are used as examples for illustration. Moreover, the results on the application of dimensional synthesis are discussed.