Type Synthesis of Self-Alignment Parallel Ankle Rehabilitation Robot with Suitable Passive Degrees of Freedom

Liu, Ya; Lu, Wenjuan; Fan, Dabao; Tan, Weijian; Hu, Bo; Zeng, Daxing

doi:10.1186/s10033-024-00996-9

Chinese Journal of Mechanical Engineering

Table 2 Subactive and passive kinematic pairs of PSAARR

From: Type Synthesis of Self-Alignment Parallel Ankle Rehabilitation Robot with Suitable Passive Degrees of Freedom

Category	Subactive kinematic pair	Passive kinematic pair	Type	Quantity
2R3P	R_sa	Non-existent	Non-existent	0
	P_sa	\(\text{PP}\hat{\text{R}}\hat{\text{R}}\)	\(\left( {\text{P}_{{{\text{sa}}}} \text{PP}} \right)\hat{\text{R}}\hat{\text{R}}\)	3
	P_sa	\(\left( {\left( {\overline{\text{P}}{\tilde{\text{P}}}\text{R}_{1} } \right)\text{R}} \right)\)	\(\left( {\left( {\dot{\text{P}}_{{{\text{sa}}}} \overline{\text{P}}\tilde{\text{P}}\text{R}_{1} } \right)\text{R}} \right)\)	24
3R2P	R_sa	\(\text{PP}\hat{\text{R}}\hat{\text{R}}\)	\(\left( {R_{{1{\text{sa}}}} \text{PP}} \right)\hat{\text{R}}_{1} \hat{\text{R}}\)	3
	R_sa	\(\left( {\left( {\overline{\text{P}}{\tilde{\text{P}}}\text{R}_{1} } \right)\text{R}} \right)\)	\(\left( {\left( {\overline{\text{P}}{\tilde{\text{P}}}\text{R}_{1} } \right)\left( {\text{R}_{2} \text{R}_{{2{\text{sa}}}} } \right)} \right)\)	12
	P_sa	\(\left( {\left( {\overline{\text{P}}\text{R}_{1} \text{R}_{1} } \right)\text{R}} \right)\)	\(\left( {\left( {{\dot{\text{P}}}_{{{\text{sa}}}} {\overline{\text{P}}\text{R}}_{{1}} {\text{R}}_{{1}} } \right){\text{R}}} \right)\)	24
4R1P	R_sa	\(\left( {\left( {\overline{\text{P}}R_{1} R_{1} } \right)R} \right)\)	\(\left( {\left( {\overline{\text{P}}R_{1} R_{1} } \right)\left( {R_{2} R_{{2{\text{sa}}}} } \right)} \right)\)	12
4R1P	P_sa	\(\left( {\left( {{\text{R}}_{{1}} {\text{R}}_{{1}} {\text{R}}_{{1}} } \right){\text{R}}} \right)\)	\(\left( {\left( {\dot{\text{P}}_{{{\text{sa}}}} {\text{R}}_{{1}} {\text{R}}_{{1}} {\text{R}}_{{1}} } \right){\text{R}}} \right)\)	8
5R	R_sa	\(\left( {\left( {{\text{R}}_{{1}} {\text{R}}_{{1}} {\text{R}}_{{1}} } \right){\text{R}}} \right)\)	\(\left( {\left( {{\text{R}}_{{1}} {\text{R}}_{{1}} {\text{R}}_{{1}} } \right)\left( {{\text{R}}_{2} {\text{R}}_{{{\text{2sa}}}} } \right)} \right)\)	4

Note: (i) R₂R₂ indicates that the axes of the revolute pairs were parallel, (ii) \(\dot{{\text{P}}}\) indicates that the axis of the prismatic pair was not perpendicular to that of the revolute pair R₁, (iii) Points (i) and (ii) are equally valid in the following

Back to article page