# TableĀ 18 Limb design of GF expressions

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