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TableĀ 3 Intersection limb expressions of GF14

From: Type Synthesis of Walking Robot Legs

Limb expression Rotation Constraint Candidate Number limitation
\({\text{G}}_{\text{F1}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{R}}_{{{\upgamma }}} } \right)\) Complete \(\overline{{{\text{G}}_{\text{F}} }} \left( { 0 , 0 , 0 , 0 , 0 , 0} \right)\) Y /
\({\text{G}}_{\text{F2}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , 0} \right)\) Complete \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{R}}_{{{\upgamma }}} }} , 0 , 0 , 0 , 0 , 0} \right)\) Y /
\({\text{G}}_{\text{F3}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , 0 , 0} \right)\) Incomplete \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{T}}_{\text{b}} }} ,\overline{{{\text{T}}_{\text{c}} }} , 0 , 0 , 0 , 0} \right)\) Y < 2
\({\text{G}}_{\text{F10}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , 0 , 0} \right)\) Incomplete \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{T}}_{\text{c}} }} ,\overline{{{\text{R}}_{{{\upgamma }}} }} , 0 , 0 , 0 , 0} \right)\) N /
\({\text{G}}_{\text{F14}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{T}}_{\text{a}} , 0 , 0 , 0} \right)\) Incomplete \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{T}}_{\text{b}} }} ,\overline{{{\text{T}}_{\text{c}} }} ,\overline{{{\text{R}}_{{{\upgamma }}} }} , 0 , 0 , 0} \right)\) Y < 2
\({\text{G}}_{\text{F23}}^{\text{III}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{R}}_{{{\upgamma }}} ,0} \right)\) Partially complete \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{T}}_{\text{c}} }} , 0 , 0 , 0 , 0 , 0} \right)\) N /
\({\text{G}}_{\text{F25}}^{\text{III}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{R}}_{{{\upbeta }}} , 0,0} \right)\) Partially complete \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{T}}_{\text{c}} }} ,\overline{{{\text{R}}_{{{\upgamma }}} }} , 0 , 0 , 0 , 0} \right)\) N /