A Coordinate-Free Approach to the Design of Generalized Griffis-Duffy Platforms

Architectural singularity belongs to the Type II singularity, in which a parallel manipulator (PM) gains one or more degrees of freedom and becomes uncontrollable. PMs remaining permanently in a singularity are beneficial for linear-to-rotary motion conversion. Griffis-Duffy (GD) platform is a mobil...

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Bibliographic Details
Published in:Chinese journal of mechanical engineering 2024-05, Vol.37 (1), p.53-9, Article 53
Main Authors: Shen, Chengwei, Pei, Xu, Hang, Lubin, Yu, Jingjun
Format: Article
Language:English
Subjects:
Coordinate-free determination
Electrical Machines and Networks
Electronics and Microelectronics
Engineering
Engineering Thermodynamics
Generalized Griffis-Duffy platforms
Geometric transformation
Heat and Mass Transfer
Instrumentation
Inversion
Machines
Manipulator design
Manufacturing
Mechanical Engineering
Mechanism and Robotics
Original Article
Platforms
Power Electronics
Processes
Rotation
Self-motion
Singularities
Theoretical and Applied Mechanics
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Summary:Architectural singularity belongs to the Type II singularity, in which a parallel manipulator (PM) gains one or more degrees of freedom and becomes uncontrollable. PMs remaining permanently in a singularity are beneficial for linear-to-rotary motion conversion. Griffis-Duffy (GD) platform is a mobile structure admitting a Bricard motion. In this paper, we present a coordinate-free approach to the design of generalized GD platforms, which consists in determining the shape and attachment of both the moving platform and the fixed base. The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints. Owing to the inversion, hidden in the geometric structure of these single-loop mechanisms, the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion, and describes the shape and attachment of the generalized GD platform. Moreover, the center of inversion not only identifies the location of rotation axis, but also affects the shape of the platform mechanism. A graphical construction of generalized GD platforms using inversion, proposed in the paper, provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.
ISSN:2192-8258
1000-9345
2192-8258
DOI:10.1186/s10033-024-01032-6