Kinematic Synthesis

This paper discusses the use of concepts of finite rigid body kinematics as well as kinematic synthesis in non-rigid, engineering folding problems. The exemplary task consists in designing a folding pattern, which allows to fold a circular sheet from a flat unfolded state into a prescribed compact spatial configuration that forms a hexagonal prism. Other two-configuration design problems may be found for instance in space applications where membranes in tensegrity reflector antennas need to be stowed in a spacecraft. The folding motion could be actuated using an appropriately designed linkage mechanism attached to the membrane, which, however, is not considered in this paper. The specific result of this work is a creative but systematic and computational procedure for crease pattern design. The approach is essentially based on the relative kinematics equations of serial kinematic chains and the finite position synthesis of linkage building blocks. These techniques sucessively combine to segment a flat bounded surface, such that it can reach the prescribed spatial configuration.

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Kinematic synthesis of adjustable moving pivot four-bar mechanisms for multi-phase motion generation

Mechanism and Machine Theory ◽

10.1016/0094-114x(95)00085-d ◽

1996 ◽

Vol 31 (4) ◽

pp. 459-474 ◽

Cited By ~ 23

Author(s):

Shao Jie Wang ◽

Raj S. Sodhi

Keyword(s):

Motion Generation ◽

Kinematic Synthesis ◽

Multi Phase ◽

Phase Motion

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Geometric Design of Symmetric 3-RRS Constrained Parallel Platforms

Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2004-59792 ◽

2004 ◽

Cited By ~ 3

Author(s):

Eric Wolbrecht ◽

Hai-Jun Su ◽

Alba Perez ◽

J. Michael McCarthy

Keyword(s):

Geometric Design ◽

Homotopy Continuation ◽

Total Degree ◽

Polynomial Equations ◽

Dimensional Synthesis ◽

Kinematic Synthesis ◽

Real Solutions ◽

Parallel Platform ◽

Three Degree Of Freedom ◽

Serial Chains

The paper presents the kinematic synthesis of a symmetric parallel platform supported by three RRS serial chains. The dimensional synthesis of this three degree-of-freedom system is obtained using design equations for each of three RRS chains obtained by requiring that they reach a specified set of task positions. The result is 10 polynomial equations in 10 unknowns, which is solved using polynomial homotopy continuation. An example is provided in which the direction of the first revolute joint (2 parameters) and the z component of the base and platform are specified as well as the two task positions. The system of polynomials has a total degree of 4096 which means that in theory it can have as many solutions. Our example has 70 real solutions that define 70 different symmetric platforms that can reach the specified positions.

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Kinematic Synthesis of an RS-SRR-SS Adjustable Spatial Motion Generator for Three Alternate Tasks

19th Design Automation Conference: Volume 2 — Design Optimization; Geometric Modeling and Tolerance Analysis; Mechanism Synthesis and Analysis; Decomposition and Design Optimization ◽

10.1115/detc1993-0381 ◽

1993 ◽

Author(s):

Jin Yao ◽

Liju Xu ◽

Shou-wen Fan

Keyword(s):

Mathematical Model ◽

Spatial Motion ◽

Kinematic Synthesis ◽

Inversion Theory ◽

Constant Distance ◽

And Inversion ◽

Distance Conditions ◽

Motion Generator

Abstract A method is presented for kinematical synthesis of an RS-SRR-SS adjustable spatial motion generator for three alternate tasks. Three separate systems of synthesis equations to exactly generate the first and the last positions for each task are obtained for the R-S by co-plane and constant distance conditions, for the S-R-R by co-plane, constant distance conditions and inversion theory, and for S-S by constant distance condition. Based on these equations, mathematical model for approximately generating the intermediate positions for each task is formulated. This method is characterized by reduction of the unknowns and equations in both exact and approximate syntheses. As a result, computing work is to be decreased obviously.

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