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TableĀ 7 Candidate limbs of GF4

From: Type Synthesis of Walking Robot Legs

Limb expression No. of cons. Cons. Lim.
\({\text{G}}_{\text{F4}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , 0 , 0 , 0} \right)\) 3 \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{R}}_{{{\upalpha }}} }} ,\overline{{{\text{R}}_{{{\upbeta }}} }} ,\overline{{{\text{R}}_{{{\upgamma }}} }} , 0 , 0 , 0} \right)\) 1
\({\text{G}}_{\text{F1}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{R}}_{{{\upgamma }}} } \right)\) 0 \(\overline{{{\text{G}}_{\text{F}} }} \left( { 0 , 0 , 0 , 0 , 0 , 0} \right)\) /
\({\text{G}}_{\text{F2}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , 0} \right)\) 1 \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{R}}_{{{\upgamma }}} }} , 0 , 0 , 0 , 0 , 0} \right)\) /
\({\text{G}}_{\text{F3}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , 0 , 0} \right)\) 2 \(\overline{{{\text{G}}_{\text{F}} }} \left( {\overline{{{\text{R}}_{{{\upbeta }}} }} ,\overline{{{\text{R}}_{{{\upgamma }}} }} , 0 , 0 , 0 , 0} \right)\) /