# Table 4 Motion/force transmission performance of the closed-loop structure of the grasping module

Type of grasping module

Expression of $$\user2{\ }_{{\text{T}}}$$

Variable range

$$\chi {\text{ = min}}\left\{ {\varsigma ,\sigma } \right\}$$

$${\varvec{\varGamma}}$$

PRRR_P

$$\user2{\ }_{{\text{T}}} = \left( {\begin{array}{*{20}c} {x_{2} - x_{1} } & {y_{2} } & {0;} & 0 & 0 & {x_{1} y_{2} } \\ \end{array} } \right)$$

$$\theta \in \left[ {45^\circ ,90^\circ } \right]$$

$${\text{min}}\left\{ {\frac{2\sqrt 3 }{3}\left| {\cos \left( {\gamma + \theta } \right)} \right|,\sin \gamma } \right\}$$

0.8803

PRPR_P

$$\user2{\ }_{{\text{T}}} = \left( {\begin{array}{*{20}c} { - \sin \gamma } & {\cos \gamma } & {0;} & 0 & 0 & {\frac{{y_{1} }}{\sin \gamma }} \\ \end{array} } \right)$$

$$\gamma \in \left[ {45^\circ ,90^\circ } \right]$$

$${\text{min}}\left\{ {\sin \gamma ,\frac{1}{\sqrt 2 \sin \gamma }} \right\}$$

0.7563

PPP_P

$$\user2{\ }_{{\text{T}}} = \left( {\begin{array}{*{20}c} { - y_{1} } & {x_{1} } & {0;} & 0 & 0 & 0 \\ \end{array} } \right)$$

$$x_{1} \in \left[ {0,l_{2o} \sin \gamma } \right]$$

$${\text{min}}\left\{ {1,\frac{{x_{1} }}{{l_{2o} \sin \gamma }}} \right\}$$

0.5000

PRRP_P

$$\user2{\ }_{{\text{T}}} = \left( {\begin{array}{*{20}c} { - x_{1} } & {y_{2} } & {0;} & 0 & 0 & {x_{1} y_{2} } \\ \end{array} } \right)$$

$$\gamma \in \left[ {45^\circ ,90^\circ } \right]$$

$${\text{min}}\left\{ {\sqrt 2 \cos \gamma ,\sin \gamma } \right\}$$

0.4957