Computer-Aided Kinematic Analysis of Planar Mechanisms Based on Symbolic Pattern Matching of Independent Kinematic Loops

1990 ◽  
Vol 112 (3) ◽  
pp. 337-346 ◽  
Author(s):  
Wei-Hua Chieng ◽  
D. A. Hoeltzel
Keyword(s):  
Pattern Matching ◽  
Kinematic Analysis ◽  
Closed Form Solution ◽  
Form Solution ◽  
New Approach ◽  
Planar Mechanism ◽  
Solution Methods ◽  
Kinematic Loops ◽  
Automatic Mechanism ◽  
Kinematic Loop

Based on a problem decomposition strategy and a symbolic kinematic loop pattern matching technique, a new method for planar mechanism kinematic analysis has been uncovered. Since this approach directly applies an analytical, closed form solution methodology to the planar mechanism kinematics problem, a number of significant advantages over other solution methods have been observed. Firstly, when applicable, this new approach requires significantly less cpu time as compared with traditional numerical methods, making timely mechanism animation feasible. Secondly, the new approach eliminates the effect of computer truncation error, thereby eliminating numerical approximation errors. Finally, it can be used to search for initial positions of planar mechanism with specified dimensions, thereby enabling automatic mechanism sketching.

A New Approach to the Control Design of Fuzzy Dynamical Systems

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ye-Hwa Chen
Keyword(s):  
Dynamical Systems ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Control Design ◽  
Form Solution ◽  
Bottom Line ◽  
New Approach ◽  
Fuzzy Dynamical System ◽  
The Cost ◽  
Fuzzy Dynamical Systems

A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

Closed-Form Inverse Kinematic Analysis of Variable-Geometry Truss Manipulators

1992 ◽  
Vol 114 (3) ◽  
pp. 438-443 ◽  
Author(s):  
B. Padmanabhan ◽  
V. Arun ◽  
C. F. Reinholtz
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Practical Importance ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Variable Geometry ◽  
Inverse Kinematic Problem ◽  
Inverse Kinematic Analysis ◽  
Variable Geometry Truss

A variety of applications for variable-geometry truss manipulators (VGTMs) have been demonstrated or proposed in the literature. Most of these applications require solution to the inverse kinematic problem, yet only a few isolated examples of closed-form solution methods have been presented to date. This paper provides an overview to the general problem of inverse kinematic analysis of variable-geometry truss manipulators and presents new closed-form solution techniques for problems of practical importance.

Rupture Instability of Plane Membranes and Solids

1960 ◽  
Vol 27 (3) ◽  
pp. 501-504
Author(s):  
S. F. Borg
Keyword(s):  
Closed Form ◽  
Continuum Mechanics ◽  
Closed Form Solution ◽  
Practical Interest ◽  
Form Solution ◽  
Compatibility Conditions ◽  
New Approach ◽  
Conservation Equations ◽  
Dynamic Phenomena

A fundamentally new approach to the rupture-fracture problem is presented. Because of the particular type of dynamic phenomena being investigated, the formulation is given in terms of the conservation equations of continuum mechanics instead of in the usual elasticity-plasticity relations. The introduction of a similarity co-ordinate permits a complete closed-form solution to a particular problem of practical interest subject to certain compatibility conditions which depend upon the specific properties of the material under consideration.

scholarly journals A Parallel Manipulator with Planar Configurable Platform and Three End-Effectors

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Jesus H. Tinajero-Campos
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Terminal Link ◽  
Planar Parallel Manipulator ◽  
End Effectors ◽  
Newton Homotopy

This work reports on the kinematic analysis of a planar parallel manipulator endowed with a configurable platform assembled with six terminal links serially connected by means of revolute joints. This topology allows the robot manipulator to dispose of three relative degrees of freedom owing to the mobility of an internal closed-loop chain. Therefore, the proposed robot manipulator can admit three end-effectors. The forward displacement analysis of the configurable planar parallel manipulator is easily achieved based on unknown coordinates denoting the pose of each terminal link. Thereafter, the analysis leads to twelve quadratic equations which are numerically solved by means of the Newton homotopy method. Furthermore, a closed-form solution is available for the inverse position analysis. On the contrary, the instantaneous kinematics of the robot manipulator is investigated by means of the theory of screws. Numerical examples are included with the purpose to illustrate the method of kinematic analysis.

Structural Error Synthesis of a Four-Bar Function Generator Using the Reliability Concept

1984 ◽  
Vol 198 (2) ◽  
pp. 87-90 ◽  
Author(s):  
A K Khare ◽  
A C Rao
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimization Techniques ◽  
Function Generator ◽  
New Approach ◽  
Numerical Example ◽  
Structural Error ◽  
Synthesis Of Mechanisms

Structural error synthesis of mechanisms is usually carried out either by the precision point approach or by using optimization techniques. A new approach for such problems using the reliability concept is presented in this paper. Besides being simple, this approach leads to a closed form solution and the mechanism can be designed to perform with any desired reliability. Its application is illustrated by means of a numerical example and the results are compared with those available.

scholarly journals Closed-Form Solution to the Position Analysis of Watt–Baranov Trusses Using the Bilateration Method

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Nicolás Rojas ◽  
Federico Thomas
Keyword(s):  
Closed Form ◽  
Characteristic Polynomial ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations ◽  
Characteristic Polynomials ◽  
Position Analysis ◽  
Exact Position ◽  
Kinematic Loops ◽  
First Time

The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial almost invariably involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. The use of kinematic loops to this end has seldom been questioned despite deriving the characteristic polynomial from them requires complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, the bilateration method has recently been used to obtain the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations nor trigonometric substitutions and using no other tools than elementary algebra. This paper shows how this technique can be applied to members of a family of Baranov trusses resulting from the circular concatenation of the Watt mechanism irrespective of the resulting number of kinematic loops. To our knowledge, this is the first time that the characteristic polynomial of a Baranov truss with more that five loops has been obtained, and hence, its position analysis solved in closed form.

On the buckling analysis of isotropic, transversely isotropic, and laminated rectangular plates via Reddy plate theory: an exact closed-form procedure

2011 ◽  
Vol 226 (5) ◽  
pp. 1210-1224 ◽  
Author(s):  
Sh Hosseini-Hashemi ◽  
S R Atashipour ◽  
M Fadaee
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Third Order ◽  
Solution Methods

Based on Reddy's third-order shear deformation theory, an exact closed-form solution is proposed to describe linear buckling of transversely isotropic laminated rectangular plates under either mono- or bi-axial compressive in-plane loads. To this end, the coupled governing equations are exactly converted to two sets of uncoupled equations for in-plane and transverse deformations of symmetric laminated plates. The new uncoupled equations are analytically solved by applying both Navier and Lévy-type solution methods. The validity and high accuracy of the current exact solution are evaluated by comparing the present results with their counterparts reported in literature.

Development and Kinematic Position Analysis of a Novel Class 2 Tensegrity Robot

2018 ◽  
Author(s):  
Carlos G. Manríquez-Padilla ◽  
Karla A. Camarillo-Gómez ◽  
Gerardo I. Pérez-Soto ◽  
Juvenal Rodríguez-Reséndiz ◽  
Carl D. Crane
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Novel ◽  
Universal Joint ◽  
Position Analysis ◽  
Experimental Prototype ◽  
Inverse Position Analysis ◽  
Kinematic Position

This paper presents a novel class 2 tensegrity robot which has contact between its rigid elements with a universal joint. Also, an strategy to obtain the forward and inverse position kinematic analysis using the parameters Denavit–Hartenberg in the distal convention is presented, obtaining the closed–form solution for the inverse position analysis and it was validated through simulation where a point of the robot followed the desired trajectory. Finally, the results were implemented in the experimental prototype of the novel class 2 tensegrity robot.

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