Research Article

Type Synthesis of 2T1R Decoupled Parallel Mechanisms Based on Lie Groups and Screw Theory

Table 1

The equivalent limbs of 2T1R PMs.

GeneratorEquivalent limbs

,  ,  ,  ,  ,  ,  ,  

,  ,  ,  ,  ,  ,  ,  
,,  

,  ,  ,  ,  ,  ,  ,  , 
,  ,  ,  ,  ,  ,  ,  , 
,  ,  ,  ,  ,  ,  ,  
,  ,  ,  ,  ,  ,  ,  
,  ,  ,  ,  ,  ,  ,  ,  
,  ,  ,  ,  ,  ,  ,  ,  
,  ,  ,  ,  ,  ,  

,  ,  ,  ,  ,  ,  
,  ,  ,  ,  ,  ,  ,  
,  ,  ,  ,  

,  ,  ,  ,  ,  ,  
,  ,  ,  ,  ,  ,  
,  ,  ,  ,  ,  

Note. (1)  , , , and stand for revolute, prismatic, cylindrical, and universal joint and stands for parallelogram loop pair. (2) The notation of black body represents the planar joints. (3) The internal joint of can be arbitrary in order.