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Table 1 Elemental representation of atlas

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

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
\( {\$ } = (0 ; { }{\mathbf{S}}) \)
  1. In the table, \( {\$}^{r} \) and \( {\$ } \) are the spiral expressions of constraints and movements