scholarly journals Discussion: “Closed Form Displacement Relationships of Single and Multi-Loop Six-Link Spatial Mechanisms” (Soni, A. H., Dukkipati, R. V., and Huang, M., 1973, ASME J. Eng. Ind., 95, pp. 709–716)

1974 ◽  
Vol 96 (2) ◽  
pp. 701-702
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Closed Form ◽  
Spatial Mechanisms

Kinematic Analysis of Spatial Mechanisms Via Successive Screw Displacements

1975 ◽  
Vol 97 (2) ◽  
pp. 739-747 ◽  
Author(s):  
Dilip Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Closed Loop ◽  
Displacement Velocity ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Straight Line ◽  
Unified Method

A new, unified method is proposed and demonstrated to conduct kinematic analysis of spatial mechanisms involving revolute, cylindrical, prismatic, helical and spherical pairs. The paper derives the equations for the successive screw displacements, and the equations for pair constraints. Using these equations, closed-form relationships for displacement, velocity and acceleration of single or multi-loop spatial mechanisms are obtained by (1) breaking the mechanism at a critical joint (2) unfolding the mechanism along a straight line (3) providing successive screw displacement at each joint and (4) reassembling the mechanism to form a closed loop. The application of this newly developed approach is demonstrated by considering an example of a two-loop spatial mechanism with revolute, cylindrical and spherical pairs.

Closed Form Displacement Relationships of Single and Multi-Loop Six-Link Spatial Mechanisms

1973 ◽  
Vol 95 (3) ◽  
pp. 709-716 ◽  
Author(s):  
A. H. Soni ◽  
R. V. Dukkipati ◽  
M. Huang
Keyword(s):  
Closed Form ◽  
Single Loop ◽  
Spatial Mechanisms

Using (3 × 3) matrices with dual elements, two loop Watt and Stephenson type six-link spatial mechanisms with one revolute and six cylinder pairs and single loop R-C-R-R-P-R, R-C-R-R-R-R six-link mechanisms are examined to obtain closed form displacement relationships between independent and dependent displacement parameters. Displacement analyses are performed to illustrate the use of these displacement relationships.

Closed Form Solutions for Connectivity and Connectivity of Motion in Mechanisms

2000 ◽  
Author(s):  
D. Kohli ◽  
N. Razmara ◽  
A. K. Dhingra
Keyword(s):  
Graph Theory ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Open Chain ◽  
Closed Loops ◽  
Closed Form Solutions ◽  
Spatial Mechanisms ◽  
Special Arrangement

Abstract This paper presents a closed form solution for determining connectivity between any two links in mechanism. The formulation is based on graph theory and its modification. The proposed approach could be applied to both planar and spatial mechanisms including combined planar-spatial mechanisms. Further, the mechanism may have multiple closed loops and/or open-chain substructures. A new concept of Connectivity of Motion has been introduced to determine the connectivity between any two links when the mechanism under consideration has special arrangement of adjacent joints such as joints with parallel and/or intersecting axes. Four examples are presented to illustrate connectivity calculations in spatial mechanisms.

Inertia Force Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 27-32 ◽  
Author(s):  
An Tzu Yang
Keyword(s):  
Closed Form ◽  
Mechanical System ◽  
Dynamic Equation ◽  
Geometric Interpretation ◽  
Analytical Tool ◽  
Inertia Force ◽  
Force Analysis ◽  
Digital Computation ◽  
Spatial Mechanisms ◽  
Analytical Expressions

A dual dynamic equation, based on dual vectors and screw calculus, is formulated here to provide a concise analytical tool for the study of the dynamics of rigid members in any complex mechanical system. In this paper the equation is applied to inertia force analysis of an RCCC mechanism of general proportions; bearing reactions and inertia torque are obtained in closed form dual-number expressions. Such analytical expressions are more susceptible for geometric interpretation and well adapted for digital computation.

Approximated Grashof-Type Movability Conditions for RSSR Mechanisms With Force Transmission Limitations

1992 ◽  
Vol 114 (1) ◽  
pp. 74-81 ◽  
Author(s):  
J. Rastegar ◽  
Q. Tu
Keyword(s):  
Closed Form ◽  
Closed Loop ◽  
Open Loop ◽  
Approximation Technique ◽  
Force Transmission ◽  
Output Link ◽  
Link Type ◽  
Spatial Mechanisms ◽  
Loop Chain ◽  
Drag Link

Closed-form Grashof-type movability conditions are derived for closed-loop RSSR mechanisms using a geometrical approximation technique. The conditions that ensure the presence of crank-rocker and drag-link type mechanisms are derived with and without force transmission limitations. The force transmission limitations may be specified as a function of the output link angle. The accuracy of the approximated conditions is analyzed. As an example, the conditions are used to synthesize a function generating mechanism with fully rotatable crank and with various force transmission requirements. The developed technique is general, and can be applied to other similar spatial mechanisms. The application of this approach to geometrical synthesis of open-loop chain manipulators is discussed.

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.

Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms

1964 ◽  
Vol 31 (2) ◽  
pp. 300-308 ◽  
Author(s):  
A. T. Yang ◽  
F. Freudenstein
Keyword(s):  
Closed Form ◽  
Quaternion Algebra ◽  
Digital Computation ◽  
Dual Number ◽  
Spatial Mechanisms ◽  
Algebraic Expressions ◽  
Transmission Angle

Dual-number quaternion algebra has been used to obtain explicit, closed-form algebraic expressions for the displacements, velocities, velocity ratios, forces, torques, mechanical advantages, transmission angle, and locking positions in spatial four-link mechanisms having one turning pair and three turn-slides. The results have been programmed for automatic digital computation.

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