Concurrent Type and Dimensional Synthesis of Planar Mechanisms Using Graph-Theoretic Enumeration, Automatic Loop Closure Equation Generation, and Descent-Based Optimization

2011 ◽  
Author(s):  
Carl A. Nelson
Keyword(s):  
A Priori ◽  
Goal Function ◽  
Dimensional Synthesis ◽  
Planar Mechanisms ◽  
Loop Closure ◽  
Graph Theoretic ◽  
Optimal Mechanism ◽  
Spatial Mechanisms ◽  
Closure Equation

An approach to concurrent type and dimensional synthesis of planar mechanisms is presented. Using graph-theoretic enumeration of mechanisms and determination of loops, automatic loop closure equations are generated. Using constrained optimization routines based on descent methods, and given an appropriate goal function, optimal mechanism designs can be determined. These are not limited to traditional problems such as rigid-body guidance and path generation, but can be more flexibly expressed according to designer needs. This method can be effective at finding mechanism solutions when topology has not been determined a priori and may also be extensible to synthesis of spatial mechanisms. This paper presents the data flow and algorithm outline, simulation results, and examples of nonstandard synthesis problems solvable with this method.

A New Method and Automatic Generation for Dynamic Analysis of Complex Planar Mechanisms Based on the Ordered Single-Opened-Chains

1994 ◽  
Author(s):  
Jian-Qing Zhang ◽  
Ting-Li Yang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Equation ◽  
Automatic Generation ◽  
The Other ◽  
New Method ◽  
Complex Mechanism ◽  
Planar Mechanisms ◽  
Spatial Mechanisms ◽  
General Dynamic

Abstract This work presents a new method for kinetostatic analysis and dynamic analysis of complex planar mechanisms, i.e. the ordered single-opened-chains method. This method makes use of the ordered single-opened chains (in short, SOC,) along with the properties of SOC, and the network constraints relationship between SOC,. By this method, any planar complex mechanism can be automatically decomposed into a series of the ordered single-opened chains and the optimal structural decomposition route (s) can be automatically selected for dynamic analysis, the paper present the dynamic equation which can be used to solve both the kinetostatic problem and the general dynamic problem. The main advantage of the proposed approach is the possibility to reduce the number of equations to be solved simultaneously to the minimum, and its high automation as well. The other advantage is the simplification of the determination of the coefficients in the equations, and thus it maybe result in a much less time-consuming algorthem. The proposed approach is illustrated with three examples. The presented method can be easily extended to the dynamic analysis of spatial mechanisms.

ON THE COUPLER CURVE OF 3R2C LINKAGES

1998 ◽  
Vol 22 (3) ◽  
pp. 251-267
Author(s):  
H.S. Yan ◽  
W.H. Hsieh
Keyword(s):  
Algebraic Curve ◽  
Three Dimensions ◽  
Critical Properties ◽  
Dimensional Synthesis ◽  
Analytical Geometry ◽  
Loop Closure ◽  
Input And Output ◽  
Closure Equation

The purpose of this paper is to investigate the properties of the coupler curves generated by all 3R2C linkages. First, the 3x3 matrix with dual elements is used to derive the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are found by the D-H matrix. Finally, homogeneous coordinate is introduced to those displacement equations, and the order and some critical properties of the coupler curve are investigated based on the theories of algebraic curve and analytical geometry of three dimensions. In addition, RCRCR and RRCCR linkages are used as examples for illustration. Moreover, the results on the application of dimensional synthesis are discussed.

Optimum Synthesis of Multiloop Planar Mechanisms for the Generation of Paths and Rigid-Body Positions by the Linear Partition of Design Equations

1977 ◽  
Vol 99 (1) ◽  
pp. 116-123 ◽  
Author(s):  
D. H. Bhatia ◽  
C. Bagci
Keyword(s):  
Rigid Body ◽  
Mechanism Design ◽  
Industrial Applications ◽  
Planar Mechanisms ◽  
Loop Closure ◽  
Optimum Synthesis ◽  
Linear Partition ◽  
Closure Equation

The optimum synthesis of multiloop planar mechanisms for the generation of paths and rigid-body positions employing the linear partition of the design equations is presented. Design equations and their applications for the optimum synthesis of the three distinct types of the Stephenson’s six-bar mechanism for the generation of paths and rigid-body positions are presented. The optimum sets of dimensions of a mechanism are determined by minimizing the error in the loop-closure equation of the path dyad and of the loops of the mechanism. Design equations having nine to twelve unknown dimensions are presented. Industrial applications of the design equations are illustrated with design examples.

On the Coupler Curve of RCPCR Linkages

1998 ◽  
Author(s):  
Hong-Sen Yan ◽  
Wen-Hsiang Hsieh
Keyword(s):  
Algebraic Curve ◽  
Three Dimensions ◽  
Critical Properties ◽  
Dimensional Synthesis ◽  
Analytical Geometry ◽  
Loop Closure ◽  
Input And Output ◽  
Closure Equation

Abstract The purpose of this paper is to investigate the properties of the coupler curves generated by all RCPCR linkages. First, the 3 × 3 matrix with dual elements is used to establish the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are found by the D-H matrix. Finally, homogeneous coordinate is introduced to those displacement equations, and the order and some critical properties of the coupler curve are investigated based on the theories of algebraic curve and analytical geometry of three dimensions. In addition, RCPCR and RRCPC linkages are used as examples for illustrations. Moreover, the results on the application of dimensional synthesis are discussed.

On nonassembly in the optimal dimensional synthesis of planar mechanisms

2001 ◽  
Vol 21 (5) ◽  
pp. 345-354 ◽  
Author(s):  
R.J. Minnaar ◽  
D.A. Tortorelli ◽  
J.A. Snyman
Keyword(s):  
Dimensional Synthesis ◽  
Planar Mechanisms

Determination of the Instantaneous Pole Axes in Single-DOF Spherical Mechanisms

2008 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
A Algorithm ◽  
Planar Mechanisms ◽  
Spherical Mechanisms ◽  
Kinematic Behavior ◽  
General Method

In spherical mechanisms, the instantaneous pole axes play the same role as the instant centers in planar mechanisms. Notwithstanding this, they are not fully exploited to study the kinematic behavior of spherical mechanisms as the instant centers are for planar mechanisms. The first step to make their use possible and friendly is the availability of efficient techniques to determine them. This paper presents a general method to determine the instantaneous pole axes in single-dof spherical mechanisms as a function of the mechanism configuration. The presented method is directly deduced from a algorithm already proposed by the author for the determination of the instant centers in single-dof planar mechanisms.

A Method for Type Synthesis of Mechanisms Using Phase Diagrams

1994 ◽  
Author(s):  
Sio-Hou Lei ◽  
Ying-Chien Tsai
Keyword(s):  
Phase Diagram ◽  
Degrees Of Freedom ◽  
Practical Application ◽  
Type Synthesis ◽  
Planar Mechanisms ◽  
Simple Loop ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Synthesis Of Mechanisms

Abstract A method for synthesizing the types of spatial as well as planar mechanisms is expressed in this paper by using the concept of phase diagram in metallurgy. The concept represented as a type synthesis technique is applied to (a) planar mechanisms with n degrees of freedom and simple loop, (b) spatial mechanisms with single degree of freedom and simple loop, to enumerate all the possible mechanisms with physically realizable kinematic pairs. Based on the technique described, a set of new reciprocating mechanisms is generated as a practical application.

scholarly journals Estimation of the mean normal measure from flat sections

2008 ◽  
Vol 40 (01) ◽  
pp. 31-48
Author(s):  
Markus Kiderlen
Keyword(s):  
A Priori ◽  
The Other ◽  
Consistent Estimator ◽  
Random Set ◽  
Normal Measure ◽  
Mild Assumption ◽  
The Mean ◽  
Vertical Sections ◽  
Almost All

We discuss the determination of the mean normal measure of a stationary random set Z ⊂ ℝ d by taking measurements at the intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z if k ≥ 3 or if k = 2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified (i.e. an a priori guess can be confirmed or discarded) using mean normal measures of intersections with m suitably chosen planes when m ≥ ⌊d / k⌋ + 1. This even holds for almost all m-tuples of k-dimensional planes are viable for verification. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.

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