Type Synthesis of Walking Robot Legs

Xi, Da; Gao, Feng

doi:10.1186/s10033-018-0216-7

Chinese Journal of Mechanical Engineering

Table 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	/

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