Discussion: “Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms” (Yang, A. T., and Freudenstein, F., 1964, ASME J. Appl. Mech., 31, pp. 300–308)

1965 ◽  
Vol 32 (1) ◽  
pp. 222-222
Author(s):  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Quaternion Algebra ◽  
Dual Number ◽  
Spatial Mechanisms

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.

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.

Novel Methods in the Displacement Analysis of Spatial Mechanisms

1994 ◽  
Author(s):  
Ian S. Fischer
Keyword(s):  
Iterative Methods ◽  
Coordinate Transformation ◽  
Kinematic Analysis ◽  
Displacement Analysis ◽  
Dual Number ◽  
Transformation Matrices ◽  
Spatial Mechanisms ◽  
Novel Methods

Abstract An aspect of dual-number coordinate-transformation matrices is used to establish iterative methods for determining the rotational and translational displacements in the kinematic analysis of complex spatial mechanisms.

Dual Polynomials and Complex Dual Numbers for Analysis of Spatial Mechanisms

1996 ◽  
Author(s):  
Harry H. Cheng ◽  
Sean Thompson
Keyword(s):  
Numerical Solutions ◽  
Polynomial Equation ◽  
Mathematical Tool ◽  
Polynomial Equations ◽  
Dual Numbers ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Spatial Mechanisms ◽  
Language Environment

Abstract Complex dual numbers w̌1=x1+iy1+εu1+iεv1 which form a commutative ring are for the first time introduced in this paper. Arithmetic operations and functions of complex dual numbers are defined. Complex dual numbers are used to solve dual polynomial equations. It is shown that the singularities of a dual input-output displacement polynomial equation of a mechanism correspond to its singularity positions. This new method of identifying singularities provides clear physical insight into the geometry of the singular configurations of a mechanism, which is illustrated through analysis of special configurations of the RCCC spatial mechanism. Numerical solutions for dual polynomial equations and complex dual numbers are conveniently implemented in the CH language environment for analysis of the RCCC spatial mechanism. Like the dual number, the complex dual number is a useful mathematical tool for analytical and numerical treatment of spatial mechanisms.

Relative Acceleration in Spatial Mechanisms

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Ian S. Fischer
Keyword(s):  
Closed Loop ◽  
Number Representation ◽  
Automatic Computation ◽  
Dual Number ◽  
Spatial Mechanisms ◽  
Relative Acceleration ◽  
Set Up ◽  
Derivatives Of

A scheme applicable to automatic computation of the joint relative accelerations, the derivatives of joint speeds with respect to time, has been developed in the dual-number representation of the kinematics of spatial mechanisms. The equations which have been developed can be set up automatically by computer for any closed-loop mechanism of binary links. While the RCCC mechanism is given as an example, the scheme can be adapted for mechanisms with prismatic as well as revolute and cylindrical joints and can be readily further developed to consider other types of joints.

Sign in / Sign up

Export Citation Format

Share Document