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.

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.

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.

The Kinematics of Spatial Double-Triangular Parallel Manipulators

1995 ◽  
Vol 117 (4) ◽  
pp. 658-661 ◽  
Author(s):  
H. R. Mohammadi Daniali ◽  
P. J. Zsombor-Murray ◽  
J. Angeles
Keyword(s):  
Degrees Of Freedom ◽  
Quaternion Algebra ◽  
Parallel Manipulators ◽  
Numerical Examples ◽  
Six Degrees Of Freedom ◽  
Dual Number ◽  
Direct Kinematics

Two versions of spatial double-triangular mechanisms are introduced, one with three and one with six degrees of freedom. Using dual-number quaternion algebra, a formula for the direct kinematics of these manipulators is derived. Numerical examples are included.

On the Derivation of Grashof-Type Moveability Conditions With Transmission Angle Control for Spatial Mechanisms

1987 ◽  
Author(s):  
J. Rastegar
Keyword(s):  
Approximation Techniques ◽  
Link Type ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Transmission Angle ◽  
Full Rotation ◽  
Drag Link

Abstract Derivation of Grashof-type conditions for spatial mechanisms that may include transmission angle limitations are discussed. It is shown that in general, different conditions need to be derived for each one of the existing configurations of the mechanism. In the absence of any transmission angle control, the conditions would be identical for pairs of configurations. As an example, for RRRSR mechanisms, Grashof-type conditions that ensure crank rotatability, the existence of a drag link type of mechanism, single or multiple changeover points, the possibility of full rotation at intermediate revolute joints, etc., are determined. A general discussion of the problems involved in such derivations, the use of approximation techniques to overcome some of the problems, and several other related subjects are presented.

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.

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