scholarly journals Kinematic Analysis and Synthesis of Mechanisms

2021 ◽  
Author(s):  
Asok Kumar Mallik ◽  
Amitabha Ghosh ◽  
Günter Dittrich
Keyword(s):  
Kinematic Analysis ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis

Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators

1995 ◽  
Vol 117 (B) ◽  
pp. 71-79 ◽  
Author(s):  
M. Raghavan ◽  
B. Roth
Keyword(s):  
Kinematic Analysis ◽  
State Of The Art ◽  
Polynomial Systems ◽  
The State ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Systems Of Polynomial Equations ◽  
And Robotics

Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.

scholarly journals Replacement in a Plane Geared Linkage of High Kinematic Pairs with Lower Pairs

2021 ◽  
Vol 24 (3) ◽  
pp. 97-103
Author(s):  
E.G. Krylov ◽  
R.F. Valiev
Keyword(s):  
Kinematic Analysis ◽  
Practical Interest ◽  
Kinematic Chains ◽  
Replacement Method ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Long Time ◽  
Shape Irregularity ◽  
Kinematic Equivalence ◽  
Higher Kinematic Pairs

The analysis of constraints in plane mechanisms is an urgent problem in the theory of machines and mechanisms. Although kinematic pairs’ classification has been known for a long time, the issue of the conjugation of links, being at the heart of the analysis and synthesis of mechanisms and machines, is of considerable theoretical and practical interest and continues to attract scientists. One of the tasks that are solved in the process of analysis and synthesis of the structures of mechanisms is the re-placement of higher kinematic pairs by lower ones. As a rule, such a replacement is made to identify kinematic chains of zero mobility, Assur's structural groups, in a mechanism. The replacement may also aim at obtaining the necessary kinematic relations. That is because specific computational difficulties hamper the kinematic analysis of chains with higher kinematic pairs due to the relative sliding and shape irregularity of mating surfaces. Yet, the use of replacements to obtain kinematic and transmission functions is difficult due to nonisomorphism of the equivalent mechanism. Simultaneously, for mixed-type mechanisms, which include geared linkages, the equivalent replacement will allow unifying the kinematic analysis methods. The paper suggests the technology of replacing higher kinematic pairs with links with lower pairs as applied to a plane geared linkage. The technology is based on the properties of the involute of a circumference. The paper proved the structural and kinematic equivalence of such a replacement. The isomorphism of the equivalent linkage will enhance the kinematic analysis, make it possible using kinematic functions, and applying methods based on the instantaneous relative rotations of links, in particular, the Aronhold-Kennedy theorem. Another application of the replacement method presented in the paper will be the expansion of opportunities for identifying idle constraints in the mechanism.

Higher Path-Curvature Analysis in Plane Kinematics

1965 ◽  
Vol 87 (2) ◽  
pp. 184-190 ◽  
Author(s):  
F. Freudenstein
Keyword(s):  
Kinematic Analysis ◽  
Algebraic Curve ◽  
Point Contact ◽  
Rates Of Change ◽  
Curvature Analysis ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Path Curvature ◽  
Motion Characteristics

Classical kinematics furnishes us with powerful techniques for the determination of the motion characteristics of a rigid body, or “plane,” or link. The present analysis is concerned more with the motion characteristics of the path generated by a point on a link, rather than with the link as a whole. For four infinitesimal displacements, it is shown that the locus of all points on a link with a prescribed ratio of path-evolute curvature to path curvature is a higher algebraic curve, the “quartic of derivative curvature.” For five infinitesimal displacements, five points on a moving link can in general be found having five-point contact with an arbitrary, prescribed curve. For circular motion, these results reduce to the classical theories of Burmester and Mueller. Equations have been derived for the first and second rates of change of path curvature in terms of the evolutes to the path. The results are applicable to the kinematic analysis and synthesis of mechanisms and are illustrated, specifically, for the generation of involute, parabolic, and elliptic arcs.

Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators

1995 ◽  
Vol 117 (B) ◽  
pp. 71-79 ◽  
Author(s):  
M. Raghavan ◽  
B. Roth
Keyword(s):  
Kinematic Analysis ◽  
State Of The Art ◽  
Polynomial Systems ◽  
The State ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Systems Of Polynomial Equations ◽  
And Robotics

Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.

REPRESENTATIONS AND IDENTIFICATIONS OF STRUCTURAL AND MOTION STATE CHARACTERISTICS OF MECHANISMS WITH VARIABLE TOPOLOGIES

2006 ◽  
Vol 30 (1) ◽  
pp. 19-40 ◽  
Author(s):  
Hong-Sen Yan ◽  
Chin-Hsing Kuo
Keyword(s):  
Topological Structure ◽  
Topological Analysis ◽  
State Machines ◽  
Matrix Representations ◽  
Motion State ◽  
New Concepts ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Finite State ◽  
State Graphs

A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). This paper is developed for the structural and motion state representations and identifications of MVTs. For representing the topological structures of MVTs, a set of methods including graph and matrix representations is proposed. For representing the motion state characteristics of MVTs, the idea of finite-state machines is employed via the state tables and state graphs. And, two new concepts, the topological homomorphism and motion homomorphism, are proposed for the identifications of structural and motion state characteristics of MVTs. The results of this work provide a logical foundation for the topological analysis and synthesis of mechanisms with variable topologies.

scholarly journals Analysis and Synthesis of Mechanisms with Bars and Gears Used in Robots and Manipulators

2017 ◽  
Author(s):  
Relly Victoria mname Petrescu ◽  
Raffaella mname Aversa ◽  
Antonio mname Apicella ◽  
MirMilad mname Mirsayar ◽  
Samuel mname Kozaitis ◽  
...  
Keyword(s):  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis

Kinematic Analysis and Synthesis of Three-Input, Eight-Bar Mechanisms Driven by Relatively Small Cranks

1992 ◽  
Author(s):  
Kambiz Farhang ◽  
Partha Sarathi Basu
Keyword(s):  
Nonlinear Equations ◽  
Kinematic Analysis ◽  
Linear Equations ◽  
Output Link ◽  
Analysis And Design ◽  
Constraint Equations ◽  
Analysis And Synthesis ◽  
The Mean ◽  
Approximate Equations

Abstract Approximate kinematic equations are developed for the analysis and design of three-input, eight-bar mechanisms driven by relatively small cranks. Application of a method in which an output link is presumed to be comprised of a mean and a perturbational motions, along with the vector loop approach facilitates the derivation of the approximate kinematic equations. The resulting constraint equations are, (i) in the form of a set of four nonlinear equations relating the mean link orientations, and (ii) a set of four linear equations in the unknown perturbations (output link motions). The latter set of equations is solved, symbolically, to obtain the output link motions. The approximate equations are shown to be effective in the synthesis of three-input, small-crank mechanisms.

Analysis and Synthesis of Linear Transmission Mechanisms: Coupled Mechanisms and Mechanisms Wth Prismatic Joints

1994 ◽  
Author(s):  
Sun-Lai Chang
Keyword(s):  
Open Loop ◽  
Joint Motion ◽  
Transmission Mechanisms ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Prismatic Joints ◽  
Application Potential ◽  
Loop Chain

Abstract The characteristics of linear transmission mechanisms are studied. Using the characteristics, the kinematic and synthesis of linear transmission mechanisms are expanded. First, the synthesis of mechanisms with prismatic joints in the equivalent open-loop chain is developed. Then the kinematics and synthesis of mechanisms with coupled joint motion are also derived. Two coupled mechanisms are used as examples to demonstrate the application potential in the industry.

SDAMP: Software for the Design and Analysis of Mechanical Presses

2000 ◽  
Author(s):  
Herbert E. Stumph ◽  
Andrew P. Murray
Keyword(s):  
Kinematic Analysis ◽  
Kinematic Synthesis ◽  
Link Mechanism ◽  
Mechanical Press ◽  
Analysis And Synthesis ◽  
Drag Link ◽  
Mechanism Kinematic ◽  
Functioning Mechanism

Abstract In this paper we introduce the MATLAB-based SDAMP (pronounced stamp) software for the analysis and synthesis of several mechanical press linkages. These linkages include the slider-crank and the four six-bar mechanisms formed by attaching a drag-link, crank-rocker, crank-shaper or Whitworth mechanism to a slider-crank. SDAMP performs four basic tasks: guided layout, kinematic analysis, mechanism refine and kinematic synthesis. Guided layout leads the user through joint selection to ensure a functioning mechanism. Kinematic analysis displays the position, velocity, acceleration and jerk of the sliding output versus the rotation of the input link. Mechanism refine allows the user to vary the geometry of an existing mechanism towards the goal of achieving a desired kinematic analysis. Lastly, kinematic synthesis determines the set of defect-free slider-cranks capable of achieving four precision points. All of these capabilities are integrated through a host of GUI driven MATLAB files in SDAMP.

A General Method for Kineto-Elastodynamic Analysis and Synthesis of Mechanisms

1972 ◽  
Vol 94 (4) ◽  
pp. 1193-1205 ◽  
Author(s):  
A. G. Erdman ◽  
G. N. Sandor ◽  
R. G. Oakberg
Keyword(s):  
Dynamic Error ◽  
Viscous Friction ◽  
Body Motion ◽  
Analysis Technique ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
External Loads ◽  
System Inertia ◽  
General Method ◽  
Internal Body

Kineto-elastodynamics is the study of the motion of mechanisms consisting of elements which may deflect due to external loads or internal body forces. This paper describes the initial phases in the development of a general method of kineto-elastodynamic analysis and synthesis based on the flexibility approach of structural analysis, which may be applied to any planar or spatial mechanism. Dynamic error is investigated due to flexural, longitudinal, and torsional element strain, and system inertia fluctuations; the treatment of Coulomb and viscous friction is indicated. Kineto-Elastodynamic Stretch Rotation Operators are derived which will rotate and stretch both planar and spatial link vectors reflecting rigid body motion plus elastic deformations of the link. A numerical example is presented to demonstrate the elastodynamic analysis technique.

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