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TableĀ 18 Limb design of GF expressions

From: Type Synthesis of Walking Robot Legs

No. Limb GF expression DoF Kinematic pair design
1 \({\text{G}}_{\text{F1}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{R}}_{{{\upgamma }}} } \right)\) 6 UPS, RUS
2 \({\text{G}}_{\text{F2}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , 0} \right)\) 5 RRU^R
3 \({\text{G}}_{\text{F3}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , {\text{R}}_{{{\upalpha }}} , 0 , 0} \right)\) 4 RRU^
4 \({\text{G}}_{\text{F4}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{T}}_{\text{c}} , 0 , 0 , 0} \right)\) 3 P^U
5 \({\text{G}}_{\text{F5}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , {\text{R}}_{{{\upalpha }}} , 0 , 0 , 0} \right)\) 3 UR, RRR//
6 \({\text{G}}_{\text{F6}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , 0 , 0 , 0 , 0} \right)\) 2 PP
7 \({\text{G}}_{\text{F7}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , 0 , 0 , 0 , 0 , 0} \right)\) 1 P
8 \({\text{G}}_{\text{F8}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{R}}_{{{\upgamma }}} , {\text{T}}_{\text{a}} , 0 , 0} \right)\) 4 SP
9 \({\text{G}}_{\text{F10}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , 0 , 0} \right)\) 4 URR, URP, RR//^U
10 \({\text{G}}_{\text{F12}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{R}}_{{{\uplambda }}} , 0 , 0 , 0} \right)\) 3 S, RRR//
11 \({\text{G}}_{\text{F14}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{T}}_{\text{a}} , 0 , 0 , 0} \right)\) 3 UP, RR//P
12 \({\text{G}}_{\text{F16}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{T}}_{\text{a}} , {\text{T}}_{\text{b}} , 0 , 0 , 0} \right)\) 3 RPP, R^U, RRR//
13 \({\text{G}}_{\text{F18}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , 0 , 0 , 0 , 0} \right)\) 2 U, RR//
14 \({\text{G}}_{\text{F21}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , 0 , 0 , 0 , 0 , 0} \right)\) 1 R