Approximate Synthesis of Spatial Linkages

1960 ◽  
Vol 27 (1) ◽  
pp. 201-206 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Helical Motion ◽  
Second Variation ◽  
Variable Pitch ◽  
Approximate Synthesis ◽  
Spatial Linkages ◽  
Four Bar Linkage

Freudenstein’s approximate synthesis of planar four-bar linkages is generalized to spatial linkages, and the conditions under which this generalization is applicable are expressed. Three cases of synthesis of spatial linkages to generate functions of one variable between nonparallel axes are considered in detail: (a) The spherical four-bar linkage; (b) a variation of the four-bar linkage in which two turning pairs are replaced by ball-and-socket joints, a linkage which may be designed to generate arbitrary functions with up to seven accuracy points; and (c) a second variation of the four-bar linkage where three turning pairs are replaced by cylinder pairs, a linkage capable of being designed to generate a variable-pitch helical motion with three accuracy points.

Finding All Solutions to Unconstrained Nonlinear Optimization for Approximate Synthesis of Planar Linkages Using Continuation Method

1999 ◽  
Vol 121 (3) ◽  
pp. 368-374 ◽  
Author(s):  
A.-X. Liu ◽  
T.-L. Yang
Keyword(s):  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Kinematic Synthesis ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Unconstrained Nonlinear Optimization ◽  
Optimum Solution ◽  
Planar Linkages ◽  
Four Bar Linkage

Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the suitable initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and three examples are given to illustrate the advantages of the proposed method.

Four-Bar Linkages—Approximate Synthesis

1959 ◽  
Vol 81 (4) ◽  
pp. 293-296
Author(s):  
W. W. Worthley ◽  
R. T. Hinkle
Keyword(s):  
Analytical Method ◽  
Graphical Solution ◽  
Analytical Treatment ◽  
Function Generator ◽  
Approximate Synthesis ◽  
Four Bar Linkage ◽  
Arbitrary Selection ◽  
Selection Of

An analytical method for synthesizing a four-bar linkage as a function generator is presented. The method, which permits the arbitrary selection of four precision points and finite angular ranges, is based on a graphical solution. This permits a preliminary graphical investigation of the six possible linkages before selecting one for analytical treatment.

scholarly journals The Coupler Surface of the RSRS Mechanism

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Nicolas Rojas ◽  
Aaron M. Dollar
Keyword(s):  
Rigid Body ◽  
Interested Reader ◽  
Implicit Equation ◽  
Spatial Mechanism ◽  
Full Equation ◽  
Sextic Curve ◽  
Spatial Linkages ◽  
Robotic Devices ◽  
Four Bar Linkage ◽  
Two Degree Of Freedom

Two degree-of-freedom (2-DOF) closed spatial linkages can be useful in the design of robotic devices for spatial rigid-body guidance or manipulation. One of the simplest linkages of this type, without any passive DOF on its links, is the revolute-spherical-revolute-spherical (RSRS) four-bar spatial linkage. Although the RSRS topology has been used in some robotics applications, the kinematics study of this basic linkage has unexpectedly received little attention in the literature over the years. Counteracting this historical tendency, this work presents the derivation of the general implicit equation of the surface generated by a point on the coupler link of the general RSRS spatial mechanism. Since the derived surface equation expresses the Cartesian coordinates of the coupler point as a function only of known geometric parameters of the linkage, the equation can be useful, for instance, in the process of synthesizing new devices. The steps for generating the coupler surface, which is computed from a distance-based parametrization of the mechanism and is algebraic of order twelve, are detailed and a web link where the interested reader can download the full equation for further study is provided. It is also shown how the celebrated sextic curve of the planar four-bar linkage is obtained from this RSRS dodecic.

Instantaneous motion and constraint analysis of Bennett linkage

2014 ◽  
Vol 230 (3) ◽  
pp. 379-391 ◽  
Author(s):  
Xiang Liu ◽  
Jing-Shan Zhao ◽  
Zhi-Jing Feng
Keyword(s):  
Analytical Method ◽  
Degree Of Freedom ◽  
Helical Motion ◽  
Mobility Analysis ◽  
Interesting Phenomenon ◽  
Constraint Analysis ◽  
Four Bar Linkage

Bennett linkage is a well-known spatial four-bar linkage with one degree-of-freedom (DOF). Although mobility analysis of Bennett linkage has been carried out by many researchers, the type, direction and location of the instantaneous motion are seldom discussed. This paper focuses on investigating the full mobility information of Bennett linkage by using analytical method for mobility, and then addresses its extending application to a Bennett-based six-bar linkage. The result demonstrates that the instantaneous motion of Bennett linkage is always a helical motion. However, the location, direction and pitch of the helical motion are changing related to different configurations. An interesting phenomenon is that the direction of helical motion will reverse suddenly when passing through the configuration that the axes of these four links keep collinear. As an extending application, a Bennett-based six-bar linkage is discussed and its peculiar mobility is an instantaneous rotation without considering the bifurcation.

Dwell Motion From Spatial Linkages

1973 ◽  
Vol 95 (2) ◽  
pp. 511-518 ◽  
Author(s):  
A. K. Shrivastava ◽  
K. H. Hunt
Keyword(s):  
Curve Matching ◽  
Single Loop ◽  
Spatial Linkages ◽  
Four Bar Linkage ◽  
Surface Curve

The potential of single-loop spatial linkages to produce an output dwell from a rotating input is broadly surveyed. Then three comparatively simple four-bar linkage arrangements are selected, and studied in detail. The dwell characteristics of all three are viewed via surface-surface or surface-curve “matching” at a spherical pair. Attention is mainly confined to symmetric output-input motions, and the accuracy of dwell is assessed.

Optimization of Spherical Joint Attachment in Spatial Linkages

1988 ◽  
Vol 110 (4) ◽  
pp. 440-445 ◽  
Author(s):  
M. M. Stanisˇic´ ◽  
W. F. Mirusky
Keyword(s):  
Kinematic Analysis ◽  
Optimization Technique ◽  
Spherical Joint ◽  
Spatial Linkages ◽  
Four Bar Linkage

This paper presents the kinematic analysis and optimization technique required for the optimal attachment of a spherical joint (i.e., a ball in a socket) to the ground pivoted link of an RSSR spatial four-bar linkage. The optimization technique is a searching algorithm, which can be applied to the problem of optimal spherical joint attachment in other types of spatial linkages as well. This attachment optimization is necessary if the socket of the joint is to have its maximum ball retention capability. The optimization technique is illustrated by an example.

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