A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

Chinese Journal of Mechanical Engineering

Table 1 Elemental representation of atlas

Atlas elements	Physical significance	Helical vector type
	Force constraints	Line vector $ {\$ }^{r} = ({\mathbf{S}} ; { }{\mathbf{S}}_{0} ) $
	Couple constraint	Couple vector $ {\$ }^{r} = (0 ; { }{\mathbf{S}}) $
	The rotating DOF	Line vector $ {\$} = ({\mathbf{S}} ; { }{\mathbf{S}}_{0} ) $
	The moving DOF	Couple vector $ {\$ } = (0 ; { }{\mathbf{S}}) $

In the table, $ {\$}^{r} $ and $ {\$ } $ are the spiral expressions of constraints and movements

Atlas elements	Physical significance	Helical vector type
	Force constraints	Line vector \( {\$ }^{r} = ({\mathbf{S}} ; { }{\mathbf{S}}_{0} ) \)
	Couple constraint	Couple vector \( {\$ }^{r} = (0 ; { }{\mathbf{S}}) \)
	The rotating DOF	Line vector \( {\$} = ({\mathbf{S}} ; { }{\mathbf{S}}_{0} ) \)
	The moving DOF	Couple vector \( {\$ } = (0 ; { }{\mathbf{S}}) \)