Discrete Kinematic Geometry and Saddle Synthesis of Planar Linkages

1973 ◽  
Vol 95 (2) ◽  
pp. 503-510 ◽  
Author(s):  
Y. L. Sarkisyan ◽  
K. C. Gupta ◽  
B. Roth

The problem of finding the locus of points in a moving plane which best approximate a circle in N positions is studied. The approximation is one which minimizes the deviation of the sum of the square of the circle radius. Two ninth order curves, analogous to the circle point curves of the exact theory are derived and studied, and several numerical results are presented. These results can be applied to the synthesis of planar linkages.


2005 ◽  
Vol 128 (6) ◽  
pp. 1261-1271 ◽  
Author(s):  
W. Z. Guo ◽  
R. Du

Single-loop N-bar linkages that contain one prismatic joint are common in engineering. This type of mechanism often requires complicated control and, hence, understanding its mobility is very important. This paper presents a systematic study on the mobility of this type of mechanism by introducing the concept of virtual link. It is found that this type of mechanism can be divided into three categories: Class I, Class II, and Class III. For each category, the slide reachable range is cut into different regions: Grashof region, non-Grashof region, and change-point region. In each region, the rotation range of the revolute joint or rotatability of the linkage can be determined based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. Furthermore, if the prismatic joint is an active joint, the revolvability of the input revolute joint is dependent in non-Grashof region but independent in other regions. If the prismatic joint is a passive joint, the revolvability of the input revolute joint is dependent on the offset distance of the prismatic joint. Two examples are given to demonstrate the presented method. The new method is able to cover all the cases of N-bar planar linkages with one or a set of adjoined prismatic joints. It can also be used to study N-bar open-loop planar robotic mechanisms.


1992 ◽  
Vol 114 (4) ◽  
pp. 536-541 ◽  
Author(s):  
Zine-Eddine Boutaghou ◽  
A. G. Erdman

Existing formulations predict the displacement and stresses in multi-body systems that result from known system parameters. In contrast, the proposed design methodology enables structured selection of system parameters necessary to produce desired elastic displacements, stresses, and frequencies. This design process involves the development of inverse design equations, the finite element analysis, and the design sensitivity equations to obtain converged solutions satisfying desired design constraints. Part 1 (Theory) considers the theoretical considerations involved. Part 2 (Applications) applies the methodology to design a four-bar linkage and a six-bar linkage.


Author(s):  
A. P. Murray ◽  
J. M. McCarthy

Abstract This paper formulates the design theory of planar four-bar linkages using the planar form of dual quaternions known as planar quaternions. The set of positions reachable by the floating link of a dyad is a quadratic algebraic surface called a constraint manifold. Determining the coefficients of the quadratic form defining this manifold is equivalent to setting the design parameters of the linkage. If the task of the linkage is specified as geometric constraints on the location of the floating link, then algebraic constraints are obtained on the quaternion components. We seek the coefficients of the constraint manifold that satisfies these constraints. The result is an algebraic formulation that is symmetric in its characterization of the linkage and task, and provides a versatile tool for the formulation and solution of linkage design problems.


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