Kinematic analysis of multi-loop spatial mechanisms: The five-loop case

Meccanica ◽  
1991 ◽  
Vol 26 (2-3) ◽  
pp. 101-110 ◽  
Author(s):  
R. Garziera ◽  
E. T. Hajiyev ◽  
R. Riva
Keyword(s):  
Kinematic Analysis ◽  
Spatial Mechanisms

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

Kinematic Analysis of Spatial Mechanisms by Means of Constant-Distance Equations

1972 ◽  
Vol 1 (3) ◽  
pp. 129-134 ◽  
Author(s):  
M.O.M. Osman ◽  
D. Segev
Keyword(s):  
Computer Analysis ◽  
Digital Computer ◽  
Kinematic Analysis ◽  
Dimensional Synthesis ◽  
Mobility Analysis ◽  
Rigid Link ◽  
Spatial Mechanisms ◽  
Constant Distance ◽  
Complex Mechanisms

The concept and use of constant-distance equations for the kinematic analysis of linkages are presented. The procedure is based on the fact that a constant-distance equation is formulated, wherever the distance between two pair-centers of a rigid link remains constant throughout its motion. This results in a much simpler kinematic analysis of the linkage. To illustrate the procedure and the feasibility of the method, the cases of spatial RRRR– and RGCR-mechanisms with coupler points are considered. The technique is well suited to digital computer analysis of complex mechanisms; extensions to dimensional synthesis as well as to dynamic and mobility analysis are possible.

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.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 1—Screw Coordinates

1971 ◽  
Vol 93 (1) ◽  
pp. 61-66 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein
Keyword(s):  
Numerical Methods ◽  
Motion Analysis ◽  
Kinematic Analysis ◽  
Rigid Bodies ◽  
Spatial Mechanisms ◽  
Computer Aided

The concept of screw coordinates is developed in terms of motor algebra, and applied to the kinematics and statics of rigid bodies, in particular to the computer-aided motion analysis of spatial mechanisms. The laws of the composition and transformation of screw coordinates and their application to the kinematics and statics of rigid bodies are developed. These results form the basis for the development of numerical methods for the kinematic analysis of 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.

Kinematic Analysis of Spatial Mechanisms Using Train Components

1981 ◽  
Vol 103 (4) ◽  
pp. 823-830 ◽  
Author(s):  
M. O. M. Osman ◽  
B. M. Bahgat ◽  
R. V. Dukkipati
Keyword(s):  
Mathematical Programming ◽  
Constitutive Equations ◽  
Kinematic Analysis ◽  
Numerical Examples ◽  
Spatial Mechanisms

A useful method for the kinematic analysis of spatial mechanisms is presented. For the purpose of kinematic analysis, the mechanism is treated as a consist of a number of master train components. For each master train component, geometric constitutive equations for use in kinematic analysis of mechanisms are developed. The kinematic analysis of all train components consisting the mechanism are performed as parts of the master components using a mathematical programming procedure. The analysis is followed in sequence from one train component to another as they form the entire mechanism. Numerical examples are presented to illustrate the proposed technique.

A Dual Number Approach to the Kinematic Analysis of Spatial Linkages With Dimensional and Geometric Tolerances

2004 ◽  
Author(s):  
Emanuele Cecchini ◽  
Ettore Pennestri` ◽  
Roberto Stefanelli ◽  
Leonardo Vita
Keyword(s):  
Kinematic Analysis ◽  
Tolerance Analysis ◽  
Rigid Bodies ◽  
Kinematic Modeling ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis ◽  
Spatial Linkages ◽  
Joint Clearances ◽  
First Time ◽  
Cardan Joint

Design robustness is somewhat connected to tolerances. In fact, the lower is the sensitivity of the kinematic function to the deviations of manufacturing process, the higher is the robustness of the design. In this investigation is described a tolerance analysis method based on dual vectors kinematic modeling of spatial linkages and on Monte Carlo simulation of the random variables. In the present analysis the hypothesis of rigid bodies is valid and only kinematic variables are considered in output. The method is applied to a Cardan joint modelled as an RCCC linkage with main dimensions considered as stochastic variables with Gaussian distribution. Dual vectors are well known in kinematic analysis and synthesis of spatial mechanisms. When compared with traditional vectorial methods, dual vectors show an enhanced capability to model misalignments among kinematic pairs axes. Although this is not the first time that dual vectors are used for the kinematic and dynamic analysis of spatial mechanisms with manufacturing errors, the present use of dual vectors to model joint clearances seems somewhat novel.

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