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TableĀ 17 GF expressions of kinematic pairs used in this paper

From: Type Synthesis of Walking Robot Legs

Kinematic pair Symbol DoF GF expression
Prismatic pair P 1 \({\text{G}}_{\text{F7}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , 0 , 0 , 0 , 0 , 0} \right)\)
Revolute pair R 1 \({\text{G}}_{\text{F21}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , 0 , 0 , 0 , 0 , 0} \right)\)
Cylinder pair C 2 \({\text{G}}_{\text{F20}}^{\text{II}} \left( {{\text{T}}_{\text{a}} , {\text{R}}_{{{\upalpha }}} , 0 , 0 , 0 , 0} \right)\)
Spherical pair S 3 \({\text{G}}_{\text{F12}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , {\text{R}}_{{{\upgamma }}} , 0 , 0 , 0} \right)\)
Universal pair U 2 \({\text{G}}_{\text{F18}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{R}}_{{{\upbeta }}} , 0 , 0 , 0 , 0} \right)\)
T-R universal pair U^ 2 \({\text{G}}_{\text{F20}}^{\text{II}} \left( {{\text{T}}_{\text{a}} , {\text{R}}_{{{\upalpha }}} , 0 , 0 , 0 , 0} \right)\)
R-T universal pair ^U 2 \({\text{G}}_{\text{F19}}^{\text{II}} \left( {{\text{R}}_{{{\upalpha }}} , {\text{T}}_{\text{a}} , 0 , 0 , 0 , 0} \right)\)
Parallelogram pair PR 1 \({\text{G}}_{\text{F7}}^{\text{I}} \left( {{\text{T}}_{\text{a}} , 0 , 0 , 0 , 0 , 0} \right)\)