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Table 3 Closed-loop structure of grasping module for prismatic output joint

From: A \({{\varvec{\Phi}}}\) 6-m Tunnel Boring Machine Steel Arch Splicing Manipulator

Number of intermediate kinematic pairs Types of intermediate kinematic pair Relationship to \(\omega_{i}\) and \(\omega_{o}\) Grasping module closed-loop structure
1 1P \(\omega_{o} = - \frac{{y_{P} }}{{x_{P} }}\omega_{i}\)
2 2R \(\omega_{o} = \frac{{x_{R1} - x_{R2} }}{{y_{R1} - y_{R2} }}\omega_{i}\)
2 2P \(\omega_{o} = \frac{{\left( {x_{P2} y_{P1} - x_{P1} y_{P2} } \right) \times 0}}{{\left( {x_{P2} y_{P1} - x_{P1} y_{P2} } \right) \times 0}}\omega_{i}\) \(\emptyset\): No solution to equation