scholarly journals Design Propagation in Mechanical Systems: Kinematic Analysis

1997 ◽  
Vol 119 (3) ◽  
pp. 338-345 ◽  
Author(s):  
H. Zou ◽  
K. A. Abdel-Malek ◽  
J. Y. Wang
Keyword(s):  
Graph Theory ◽  
Design Variable ◽  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Mechanical Systems ◽  
Joint Position ◽  
Closed Loops ◽  
Cartesian Space ◽  
Spatial Mechanisms ◽  
Joint Coordinates

A broadly applicable formulation for investigating design propagations in mechanisms is developed and illustrated. Analytical criteria in terms of the variations of joint position vectors and orientation matrices for planar and spatial mechanisms are presented. Mechanisms are represented using graph theory and closed loops are converted to a tree-like structure by cutting joints and introducing new constraints. The Jacobian matrix in Cartesian space is then transformed to Joint coordinates space. Two cases are considered: a pair of bodies remain connected by one joint after cutting additional joints and a pair of bodies are disconnected after cutting joints. Using this method, a designer has the ability to study the propagated effect of changing a design variable on the design. The presented formulation is validated through a numerical example of a McPherson strut suspension system. The system is analyzed and an assembled configuration is computed after a change in design.

Analytical Criteria for the Analysis of Design Propagations in Mechanisms

1996 ◽  
Author(s):  
Hong-Liu Zou ◽  
Karim Abdel-Malek ◽  
Jia-Yi Wang
Keyword(s):  
Graph Theory ◽  
Design Variable ◽  
Jacobian Matrix ◽  
Suspension System ◽  
Joint Position ◽  
Closed Loops ◽  
Numerical Example ◽  
Cartesian Space ◽  
Spatial Mechanisms ◽  
Joint Coordinates

Abstract A broadly applicable formulation for investigating design propagations in mechanisms is developed and illustrated. Analytical criteria in terms of the variations of joint position vectors and orientation matrices for planar and spatial mechanisms are presented. Mechanisms are represented using graph theory and closed loops are converted to a tree-like structure by cutting joints and introducing new constraints. The Jacobian matrix in Cartesian space is then transformed to Joint coordinates space. Two cases are considered: a pair of bodies remain connected by one joint after cutting additional joints and a pair of bodies are disconnected after cutting joints. Using this method, a designer has the ability to study the propagated effect of changing a design variable on the design. The presented formulation is validated through a numerical example of a McPherson strut suspension system. The system is analyzed and an assembled configuration is computed after a change in design.

Numerical Formulations for Computing Design Propagations of the Spatial Slider-Crank Mechanism

1996 ◽  
Author(s):  
Hong-Liu Zou ◽  
Karim Abdel-Malek ◽  
Jia-Yi Wang
Keyword(s):  
Spanning Tree ◽  
Design Parameters ◽  
Coordinate Space ◽  
Joint Position ◽  
Link Length ◽  
Closed Loops ◽  
Numerical Examples ◽  
Cartesian Space ◽  
Numerical Formulation ◽  
Crank Mechanism

Abstract A numerical formulation for studying the design of a spatial slider-crank mechanism is developed and illustrated. The mechanism is modeled using graph theory and closed loops are converted to a spanning tree structure by cutting joints and introducing new constraints. Variations of these constraints with respect to design parameters are derived. A change in link length or link orientation is propagated through the model and a new assembled configuration is computed hence redesigning the mechanism. Constraints are formulated in Cartesian space but computed in relative joint coordinate space. The Jacobian of the constraint is transformed to joint coordinate space in order to compute an assembled configuration for the cut-joint constraint formulation. The experimental code is illustrated through numerical examples where joint-position vectors and orientation matrices are altered.

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.

Some Applications of Graph Theory to the Structural Analysis of Mechanisms

1967 ◽  
Vol 89 (1) ◽  
pp. 153-158 ◽  
Author(s):  
L. Dobrjanskyj ◽  
F. Freudenstein
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Mechanical Systems ◽  
Kinematic Chains ◽  
Computerized Method ◽  
Spatial Mechanisms ◽  
Structural Identity ◽  
Computer Aided ◽  
Systematic Enumeration

Concepts in graph theory, which have been described elsewhere [2, 4, 6] have been applied to the development of (a) a computerized method for determining structural identity (isomorphism) between kinematic chains, (b) a method for the automatic sketching of the graph of a mechanism defined by its incidence matrix, and (c) the systematic enumeration of general, single-loop constrained spatial mechanisms. These developments, it is believed, demonstrate the feasibility of computer-aided techniques in the initial stages of the design of mechanical systems.

scholarly journals A Kinematical Analysis of the Flap and Wing Mechanism of a Light Sport Aircraft Using Topological Models

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1243
Author(s):  
Sorin Vlase ◽  
Ion-Marius Ghiţescu ◽  
Marius Paun
Keyword(s):  
Graph Theory ◽  
Mechanical System ◽  
Linear Systems ◽  
Kinematic Analysis ◽  
Control Mechanism ◽  
Practical Application ◽  
Dynamic Level ◽  
New Formulation ◽  
Topological Models ◽  
Independent Loops

In this, paper, we propose a method of kinematic analysis of a planar mechanism with application to the flap and wing mechanism of a light sport aircraft. A topological model is used to describe a mechanical system, which is a model that allows the study of the maneuverability of the system. The proposed algorithm is applied to determine the velocity and acceleration field of this multibody mechanical system. The graph associated with the mechanical system is generated in a new formulation and based on it, the fundamental loops of the graph are identified (corresponding to the independent loops of the mechanism), the equations for closing vectorial contours are written, and the kinematic conditions for determining velocities and accelerations and the associated linear systems are solved, which provides the field of speeds and accelerations. Graph Theory is applied at a kinematic level and not at a dynamic level, as in previous studies. A practical application for the kinematic analysis of the control mechanism of a light aircraft illustrates the proposed method.

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.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

2006 ◽  
Vol 129 (4) ◽  
pp. 390-396 ◽  
Author(s):  
Si J. Zhu ◽  
Zhen Huang ◽  
Hua F. Ding
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Rear Part ◽  
Lower Mobility ◽  
Acceleration Analysis

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N<6) mechanism, this method can build a square (N×N) Jacobian matrix and cubic (N×N×N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

A Time Variational Method for the Approximate Solution of Nonlinear Systems Undergoing Multiple-Frequency Excitations

2020 ◽  
Vol 15 (3) ◽  
Author(s):  
K. Prabith ◽  
I. R. Praveen Krishna
Keyword(s):  
Variational Method ◽  
Numerical Integration ◽  
Jacobian Matrix ◽  
Mechanical Systems ◽  
Approximation Error ◽  
System Response ◽  
Response Analysis ◽  
Multiple Frequency ◽  
Nonlinear Mechanical ◽  
Nonlinear Force

Abstract The main objective of this paper is to use the time variational method (TVM) for the nonlinear response analysis of mechanical systems subjected to multiple-frequency excitations. The system response, which is composed of fractional multiples of frequencies, is expressed in terms of a fundamental frequency that is the greatest common divisor of the approximated frequency components. Unlike the multiharmonic balance method (MHBM), the formulation of the proposed method is very simple in analyzing the systems with more than two excitation frequencies. In addition, the proposed method avoids the alternate transformation between frequency and time domains during the calculation of the nonlinear force and the Jacobian matrix. In this work, the performance of the proposed method is compared with that of numerical integration and the MHBM using three nonlinear mechanical models undergoing multiple-frequency excitations. It is observed that the proposed method produces approximate results during the quasi-periodic response analysis since the formulation includes an approximation of the incommensurate frequencies to commensurate ones. However, the approximation error is very small and the method reduces a significant amount of computational efforts compared to the other methods. In addition, the TVM is a recommended option when the number of state variables involved in the nonlinear function is high as it calculates the nonlinear force vector and the Jacobian matrix directly from the displacement vector. Moreover, the proposed method is far much faster than numerical integration in capturing the steady-state, quasi-periodic responses of the nonlinear mechanical systems.

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