Kinematic Analysis of Spatial Six-Link 3R-2P-C Mechanisms

1976 ◽  
Vol 4 (2) ◽  
pp. 71-76
Author(s):  
M.O.M. Osman ◽  
R. V. Dukkipati
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Input Output ◽  
Variable Parameters ◽  
Output Displacement ◽  
Loop Equation ◽  
Dual Number ◽  
Input And Output ◽  
Order Polynomial ◽  
Output Equation

Using (3 x 3) matrices with dual-number elements, closed-form displacement relationships are derived for a spatial six-link R-C-P-R-P-R mechanism. The input-output closed form displacement relationship is obtained as a second order polynomial in the output displacement. For each set of the input and output displacements obtained from the equation, all other variable parameters of the mechanism are uniquely determined. A numerical illustrative example is presented. Using the dual-matrix loop equation, with proper arrangement of terms and following a procedure similar to that presented, the closed-form displacement relationships for other types of six-link 3R + 2P + 1C mechanisms can be obtained. The input-output equation derived may also be used to generate the input-output functions for five-link 2R + 2C + 1P mechanisms and four-link mechanisms with one revolute and three cylinder pairs.

Closed-Form Displacement Analysis of Five-Link R-C-R-C-P Spatial Mechanism

1973 ◽  
Vol 2 (4) ◽  
pp. 238-240
Author(s):  
R. V. Dukkipati
Keyword(s):  
Closed Form ◽  
Second Order ◽  
Input Output ◽  
Variable Parameters ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Input And Output ◽  
Order Polynomial

Using (3 x 3) matrices with dual-number elements, closed-form displacement relationships are derived for a spatial five-link R-C-R-C-P mechanism. The input-output closed form displacement relationship is obtained as a second order polynomial in the output displacement. For each set of the input and output displacements obtained from the equation, all other variable parameters of the mechanism are uniquely determined. A numerical illustrative example is presented. The derived input-output relationship can be used to synthesize an R-C-R-C-P function generating mechanism for a maximum of 15 precision conditions.

Displacement Analysis of the RRCCR Five-Link Spatial Mechanism

1970 ◽  
Vol 37 (3) ◽  
pp. 689-696 ◽  
Author(s):  
M. S. C. Yuan
Keyword(s):  
Input Output ◽  
Eighth Order ◽  
Variable Parameters ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Input And Output ◽  
Displacement Equation ◽  
Order Polynomial

By the method of line coordinates, the input-output displacement equation of the RRCCR five-link spatial mechanism is obtained as an eighth-order polynomial in the half tangent of the output angle. For each set of the input and output angles obtained from the polynomial, all other variable parameters of the mechanism are uniquely determined, and the accuracy of the numerical values of each set of solutions is verified.

Displacement Analysis of the Generalized Clemens Coupling, The R-R-S-R-R Spatial Linkage

1975 ◽  
Vol 97 (2) ◽  
pp. 575-580 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Fourth Order ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Input Output ◽  
Closed Form Solutions ◽  
Input And Output ◽  
Order Polynomial ◽  
Special Case ◽  
Output Equation ◽  
Fourth Order Polynomial

The Clemens Coupling is a constant-velocity, universal-type joint for nonparallel intersecting shafts. This mechanism is a spatial linkage with five links connected by four revolute pairs, R, and one spherical pair (ball-and-socket joint), S, which is located symmetrically with respect to the input and output shafts. The Clemens Coupling is a special case of the R-R-S-R-R spatial linkage with general proportions, which will, therefore, be called the Generalized Clemens Coupling. This paper gives the algebraic derivation of the input-output equation for the general R-R-S-R-R linkage and demonstrates that it is a fourth-order polynomial in the half tangents of the crank angles. The effect of housing-error tolerances on the displacements of the Clemens Coupling has also been considered. The results demonstrate feasibility of closed-form solutions for five-link mechanisms with kinematic pairs having more than two degrees of freedom.

Displacement Analysis of the RPRCRR Six-Link Spatial Mechanism

1971 ◽  
Vol 38 (4) ◽  
pp. 1029-1035 ◽  
Author(s):  
M. S. C. Yuan
Keyword(s):  
Algebraic Equation ◽  
Input Output ◽  
Variable Parameters ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Numerical Example ◽  
Input And Output ◽  
Displacement Equation

Using the method of line coordinates, the input-output displacement equation of the RPRCRR six-link spatial mechanism is obtained as an algebraic equation of 16th order. For each set of the input and output angles obtained from the equation, all other variable parameters of the mechanism are also determined. A numerical example is presented.

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

An Automated Inversion Apporach to Closed-Form Kinematic Analysis of Planar Mechanisms

1992 ◽  
Author(s):  
Arunava Biswas ◽  
Gary L. Kinzel
Keyword(s):  
Closed Form ◽  
Iterative Methods ◽  
Kinematic Analysis ◽  
Equation Approach ◽  
Planar Mechanisms ◽  
Loop Equation ◽  
Closed Form Solutions

Abstract In this paper an inversion approach is developed for the analysis of planar mechanisms using closed-form equations. The vector loop equation approach is used, and the occurrence matrices of the variables in the position equations are obtained. After the loop equations are formed, dependency checking of the unknowns is performed to determine if it is possible to solve for any two equations in two unknowns. For the cases where the closed-form solutions cannot be implemented directly, possible inversions of the mechanism are studied. If the vector loop equations for an inversion can be solved in closed-form, they are identified and solved, and the solutions are transformed back to the original linkage. The method developed in this paper eliminates the uncertainties involved, and the large number of computations required in solving the equations by iterative methods.

Displacement Analysis of Spatial Five-Link Mechanisms Using (3×3) Matrices With Dual-Number Elements

1969 ◽  
Vol 91 (1) ◽  
pp. 152-156 ◽  
Author(s):  
A. T. Yang
Keyword(s):  
Closed Form ◽  
Algebraic Equation ◽  
Input Output ◽  
Fourth Degree ◽  
Displacement Analysis ◽  
Dual Number ◽  
Closure Equation

A closure equation, in terms of matrices with dual-number elements, for spatial five-link mechanisms, is presented in this paper. From the equation, a set of displacement equations for a RCRCR mechanism with general proportions is obtained; the input-output relationship is expressed as a fourth-degree algebraic equation and formulas to determine other linkage variables are expressed in closed form.

Displacement Analysis of a Spatial 7R Mechanism—A Generalized Lobster’s Arm

1979 ◽  
Vol 101 (2) ◽  
pp. 224-231 ◽  
Author(s):  
J. Duffy ◽  
S. Derby
Keyword(s):  
Mathematical Model ◽  
Kinematic Analysis ◽  
Input Output ◽  
Major Step ◽  
Displacement Analysis ◽  
The Mathematical Model ◽  
Output Equation

An input-output equation of degree 24 is derived for a spatial 7R mechanism with consecutive pair axes intersecting. This mechanism is essentially the mathematical model for the kinematic analysis of a lobster’s arm which is an open 6R chain with mutually perpendicular consecutive pair axes, the geometry of which was first described by Willis [4] in 1841. The analysis of this special 7R mechanism constitutes a major step towards the solution of the general 7R mechanism with seven axes arbitrarily oriented in space.

Automatic Generation of the Input-Output Equations of Planar Mechanisms

1994 ◽  
Author(s):  
Kunter A. Kanberoglu ◽  
Resit Soylu
Keyword(s):  
Closed Form ◽  
Functional Relation ◽  
Automatic Generation ◽  
Computational Effort ◽  
Input Output ◽  
Symbolic Manipulation ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Transmission Angle ◽  
Output Equation

Abstract In this article, a methodology, which yields (in closed-form) the functional relation between “any” two joint variables of a one degree-of-freedom planar mechanism, is developed. For instance, the transmission angle and crank-rotatibility synthesis algorithms (Soylu, 1993; Soylu and Kanberoğlu, 1993) require such a generic input-output equation. The equation is obtained in an optimal manner which minimizes the computational effort associated with it. The tools of theory of elimination and symbolic manipulation are also used in the developed method.

DISPLACEMENT ANALYSIS OF Ro-R-R-CP SPATIAL MECHANISMS WITH VECTOR ALGEBRAIC METHOD

1999 ◽  
Vol 23 (1A) ◽  
pp. 95-112
Author(s):  
C.M. Wong ◽  
K.C. Chan ◽  
Y.B. Zhou
Keyword(s):  
Closed Form ◽  
Algebraic Method ◽  
Input Output ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanisms ◽  
Kinematic Loop

This paper presents the displacement analysis of the three variants of a spatial kinematic loop containing 3R and 1CP joints using vector algebraic method. The closed-form input-output displacement equations of this mechanism are derived as forth-order polynomials. Analytical steps and expressions are laid out uniformly and simply.

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