Actuation Spaces Synthesis of Lower-Mobility Parallel Mechanisms Based on Screw Theory

Chinese Journal of Mechanical Engineering

Table 1 Corresponding actuation wrenches and vector $\varvec{\mu}_{k}$

Actuated pairs	Actuation wrench	Vector $\varvec{\mu}_{k}$
$R_{i}$, i=1,2,3	$\varvec{\$ }_{Ai1} = \left( {\begin{array}{*{20}c} {l_{i1} } & {m_{i1} } & {n_{i1} ;} & {p_{i1} } & {q_{i1} } & {r_{i1} } \\ \end{array} } \right)$	$\left( {\begin{array}{*{20}c} {n_{i1} } & {\mu_{2k} } & {\mu_{3k} } \\ \end{array} } \right)$
$P_{i}$, i=1,2,3	$\varvec{\$ }_{Ai2} = \left( {\begin{array}{*{20}c} {l_{i2} } & {m_{i2} } & {n_{i2} ;} & {p_{i2} } & {q_{i2} } & {r_{i2} } \\ \end{array} } \right)$	$\left( {\begin{array}{*{20}c} {n_{i2} } & {\mu_{2k} } & {\mu_{3k} } \\ \end{array} } \right)$

Actuated pairs	Actuation wrench	Vector \(\varvec{\mu}_{k}\)
\(R_{i}\), i=1,2,3	\(\varvec{\$ }_{Ai1} = \left( {\begin{array}{*{20}c} {l_{i1} } & {m_{i1} } & {n_{i1} ;} & {p_{i1} } & {q_{i1} } & {r_{i1} } \\ \end{array} } \right)\)	\(\left( {\begin{array}{*{20}c} {n_{i1} } & {\mu_{2k} } & {\mu_{3k} } \\ \end{array} } \right)\)
\(P_{i}\), i=1,2,3	\(\varvec{\$ }_{Ai2} = \left( {\begin{array}{*{20}c} {l_{i2} } & {m_{i2} } & {n_{i2} ;} & {p_{i2} } & {q_{i2} } & {r_{i2} } \\ \end{array} } \right)\)	\(\left( {\begin{array}{*{20}c} {n_{i2} } & {\mu_{2k} } & {\mu_{3k} } \\ \end{array} } \right)\)