Spatial Overconstrained Linkages—The Lost Jade

2012 ◽  
pp. 535-550 ◽  
Author(s):  
Yan Chen ◽  
Zhong You
Keyword(s):  
Overconstrained Linkages

An Investigation of Screw Systems in the Finite Displacements of Bennett-Based 6R Linkages

1999 ◽  
Vol 122 (4) ◽  
pp. 426-430 ◽  
Author(s):  
Chintien Huang ◽  
Chi-Chih Sun
Keyword(s):  
Numerical Simulations ◽  
Second Order ◽  
Finite Displacement ◽  
Finite Displacements ◽  
Overconstrained Linkages

This paper investigates, via numerical simulations, the finite displacements of all the known Bennett-based 6R overconstrained linkages: Goldberg’s 6R, variant Goldberg 6R, Waldron’s hybrid 6R, and Wohlhart’s hybrid 6R linkages. An investigation of the finite displacements of nine distinct linkages reveals that every Bennett-based 6R linkage, except for the isomerization of Wohlhart’s hybrid linkage, inherits the linear properties of the Bennett mechanism. The relative finite displacement screws of some non-adjacent links of these linkages form screw systems of the second order. Thirty-one screw systems are reported in this paper. [S1050-0472(00)02204-2]

scholarly journals A family of mixed double-Goldberg 6 R linkages

2011 ◽  
Vol 468 (2139) ◽  
pp. 871-890 ◽  
Author(s):  
C. Y. Song ◽  
Y. Chen
Keyword(s):  
Degree Of Freedom ◽  
Construction Process ◽  
Complete Family ◽  
Linkage Method ◽  
The Common ◽  
Overconstrained Linkages

A complete family of double-Goldberg 6 R linkages is reported in this article by combining a subtractive Goldberg 5 R linkage and a Goldberg 5 R linkage through the common link-pair or common Bennett-linkage method. A number of distinct types of overconstrained linkages are built, namely the mixed double-Goldberg 6 R linkages. They all have one degree of freedom and their closure equations are derived in detail. One of them degenerates into a Goldberg 5 R linkage. From the construction process and geometry conditions, the corresponding relationship between the newly found 6 R linkages and the double-Goldberg 6 R linkages, constructed from two Goldberg 5 R linkages or two subtractive Goldberg 5 R linkages, has been established.

On spatial networks of overconstrained linkages

1986 ◽  
Vol 21 (5) ◽  
pp. 427-437 ◽  
Author(s):  
J.Eddie Baker ◽  
Hu Min
Keyword(s):  
Spatial Networks ◽  
Overconstrained Linkages

Overconstrained Linkages

1979 ◽  
Vol 6 (4) ◽  
pp. 393-402 ◽  
Author(s):  
K J Waldron
Keyword(s):  
Overconstrained Linkages

A New Approach for the Orders of the Bennett-Based Linkages in Mobility Analysis

2009 ◽  
Author(s):  
Jingfang Liu ◽  
Zhen Huang ◽  
Yanwen Li
Keyword(s):  
Superposition Principle ◽  
Mobility Analysis ◽  
Linear Superposition ◽  
Geometric Properties ◽  
New Approach ◽  
Single Loop ◽  
Linear Superposition Principle ◽  
Overconstrained Linkages

Among the 3D single-loop overconstrained linkages, quite a number of them are combinations of Bennett linkages. Mobility on the overconstrained linkages including the Bennett-based linkages is known to be one of the difficult topics in kinematics. In the paper, a new approach based on the linear superposition principle for determining the orders of Bennett-based linkages is proposed, and the mobility of some typical Bennett-based linkages is calculated with the Modified Gru¨bler-Kutzbach criterion. In addition, geometric properties of some of the screw systems are employed to identify whether the mobility is global.

Construction of Overconstrained Linkages by Factorization of Rational Motions

2012 ◽  
pp. 213-220 ◽  
Author(s):  
Gábor Hegedüs ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
Overconstrained Linkages

ON THE SIMPLE STATIONARY CONFIGURATIONS OF SINGLE-LOOP SPATIAL N-REVOLUTE OVERCONSTRAINED LINKAGES

1996 ◽  
Vol 20 (1) ◽  
pp. 17-39 ◽  
Author(s):  
Chung-Ching Lee
Keyword(s):  
Computer Graphics ◽  
Differential Equations ◽  
Range Of Motion ◽  
Closed Form ◽  
Single Loop ◽  
Closed Form Solutions ◽  
Systematic Formulation ◽  
Overconstrained Linkages

Based on the derived matrix and its differential equations, a systematic formulation is presented to either identify the simple stationary configurations of movable spatial 4R, 5R and 6R overconstrained linkages or prove none of them occurs at all. Some examples are given to confirm the correctness and validity of the derived mathematical criterion. In addition, the closed-form solutions of linkage joint variables are well-established and with the help of computer graphics, geometrical meanings of linkage configurations are described. This approach can be used to provide a foundation for understanding the range of motion in overconstrained linkage application.

Sign in / Sign up

Export Citation Format

Share Document