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Table 1 Number of revolute joints under different input and output joints

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

Input and output joint types

Condition

Number of rotating pairs

\(a_{1} = a_{2} = 0\)

\(\sum\limits_{i = 1}^{l} {\omega_{Ri} } = 0\)

\(l \in \left\{ {0,2} \right\}\)

\(a_{1} = 0, a_{2} = 1\) or \(a_{1} = 1, a_{2} = 0\)

\(\sum\limits_{i = 1}^{l} {\omega_{Ri} } \ne 0\)

\(l \in \left\{ {1,2} \right\}\)

\(a_{1} = a_{2} = 1\)

\(\sum\limits_{i = 1}^{l} {\omega_{Ri} } = \omega_{o} - \omega_{i}\)

\(l \in \left\{ {0,1,2} \right\}\)