An Automated Inversion Apporach to Closed-Form Kinematic Analysis of Planar Mechanisms

22nd Biennial Mechanisms Conference: Mechanism Design and Synthesis ◽

10.1115/detc1992-0309 ◽

1992 ◽

Author(s):

Arunava Biswas ◽

Gary L. Kinzel

Keyword(s):

Closed Form ◽

Iterative Methods ◽

Kinematic Analysis ◽

Equation Approach ◽

Planar Mechanisms ◽

Loop Equation ◽

Closed Form Solutions

Abstract In this paper an inversion approach is developed for the analysis of planar mechanisms using closed-form equations. The vector loop equation approach is used, and the occurrence matrices of the variables in the position equations are obtained. After the loop equations are formed, dependency checking of the unknowns is performed to determine if it is possible to solve for any two equations in two unknowns. For the cases where the closed-form solutions cannot be implemented directly, possible inversions of the mechanism are studied. If the vector loop equations for an inversion can be solved in closed-form, they are identified and solved, and the solutions are transformed back to the original linkage. The method developed in this paper eliminates the uncertainties involved, and the large number of computations required in solving the equations by iterative methods.

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Kinematic Analysis of Spatial Six-Link 3R-2P-C Mechanisms

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1976-0012 ◽

1976 ◽

Vol 4 (2) ◽

pp. 71-76

Author(s):

M.O.M. Osman ◽

R. V. Dukkipati

Keyword(s):

Closed Form ◽

Kinematic Analysis ◽

Input Output ◽

Variable Parameters ◽

Output Displacement ◽

Loop Equation ◽

Dual Number ◽

Input And Output ◽

Order Polynomial ◽

Output Equation

Using (3 x 3) matrices with dual-number elements, closed-form displacement relationships are derived for a spatial six-link R-C-P-R-P-R mechanism. The input-output closed form displacement relationship is obtained as a second order polynomial in the output displacement. For each set of the input and output displacements obtained from the equation, all other variable parameters of the mechanism are uniquely determined. A numerical illustrative example is presented. Using the dual-matrix loop equation, with proper arrangement of terms and following a procedure similar to that presented, the closed-form displacement relationships for other types of six-link 3R + 2P + 1C mechanisms can be obtained. The input-output equation derived may also be used to generate the input-output functions for five-link 2R + 2C + 1P mechanisms and four-link mechanisms with one revolute and three cylinder pairs.

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KINEMATIC ANALYSIS AND PROTOTYPE OF A METAMORPHIC ANTHROPOMORPHIC HAND WITH A RECONFIGURABLE PALM

International Journal of Humanoid Robotics ◽

10.1142/s0219843611002538 ◽

2011 ◽

Vol 08 (03) ◽

pp. 459-479 ◽

Cited By ~ 42

Author(s):

GUOWU WEI ◽

JIAN S. DAI ◽

SHUXIN WANG ◽

HAIFENG LUO

Keyword(s):

Closed Form ◽

Matrix Equation ◽

Kinematic Analysis ◽

Structure Design ◽

Characteristic Matrix ◽

Robotic Hand ◽

Closed Form Solutions ◽

First Time

A novel metamorphic anthropomorphic hand is for the first time introduced in this paper. This robotic hand has a reconfigurable palm that generates changeable topology and augments dexterity and versatility of the hand. Structure design of the robotic hand is presented and based on mechanism decomposition kinematics of the metamorphic anthropomorphic hand is characterized with closed-form solutions leading to the workspace investigation of the robotic hand. With characteristic matrix equation, twisting motion of the metamorphic robotic hand is investigated to reveal both dexterity and manipulability of the metamorphic hand. Through a prototype, grasping and prehension of the robotic hand are tested to illustrate characteristics of the new metamorphic anthropomorphic hand.

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A one-step non-iterative solution algorithm for mechanisms—II. Application and closed-form solutions for planar mechanisms

Mechanism and Machine Theory ◽

10.1016/0094-114x(74)90035-4 ◽

1974 ◽

Vol 9 (2) ◽

pp. 169-180 ◽

Cited By ~ 3

Author(s):

M.A Townsend

Keyword(s):

Closed Form ◽

Iterative Solution ◽

Solution Algorithm ◽

Planar Mechanisms ◽

Closed Form Solutions ◽

One Step

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Kinematic Analysis of a Novel Translational Platform

Journal of Mechanical Design ◽

10.1115/1.1563637 ◽

2003 ◽

Vol 125 (2) ◽

pp. 308-315 ◽

Cited By ~ 41

Author(s):

Massimo Callegari ◽

Matteo Tarantini

Keyword(s):

Closed Form ◽

Kinematic Analysis ◽

Parallel Mechanism ◽

Simple Structure ◽

Jacobian Matrix ◽

Differential Analysis ◽

Symbolic Expression ◽

Closed Form Solutions ◽

Design Considerations ◽

Working Space

A new three-d.o.f. parallel mechanism, with 3-RPC topology, is presented in the paper and its kinematics is studied. The proposed architecture, if proper geometrical conditions are satisfied, has an overconstrained structure which allows motions of pure translation. The simple structure of the mechanism allows finding closed-form solutions for both inverse and direct position kinematics; the differential analysis has been developed as well, by deriving a symbolic expression for the Jacobian matrix. Then, some design considerations are exposed to keep the singular points out of the working space of the mechanism and all the isotropic configurations are eventually identified.

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Kinematic Analysis of Skew Cardanic Motion and the Skew Swinging-Block Linkage

23rd Biennial Mechanisms Conference: Mechanism Synthesis and Analysis ◽

10.1115/detc1994-0182 ◽

1994 ◽

Author(s):

F. Freudenstein ◽

E. J. F. Primrose ◽

Hong-Jen Chen

Keyword(s):

Algebraic Geometry ◽

Closed Form ◽

Kinematic Analysis ◽

Three Dimensional ◽

Planar Mechanisms ◽

Crank Mechanism

Abstract The classical cardanic motion and the swinging-block linkage are basic planar mechanisms. In the following investigation, the objective is the analysis of their three-dimensional (and, hence, more versatile) counterparts: the skew slider-crank mechanism and the skew swinging-block linkage. These linkages as far as we are aware, have not yet been analyzed analytically. An analysis utilizing their algebraic geometry will be instructive in determining their displacements and derivatives in closed form. This, in turn, should be useful in facilitating three-dimensional applications. With the ever-increasing sophistication in the area of mechanisms design and analysis, we believe that the time has come for the analysis of these linkages, including their algebraic geometry. This is the objective of this investigation.

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