Position Analysis of Spatial Mechanisms

1984 ◽  
Vol 106 (2) ◽  
pp. 252-255 ◽  
Author(s):  
J. Llinares ◽  
A. Page
Keyword(s):  
Computational Algorithm ◽  
Matrix Notation ◽  
Position Analysis ◽  
Spatial Mechanisms ◽  
Lower Pair ◽  
Simple Equations

In this paper matrix notation is used to develop a computational algorithm for position analysis of spatial mechanisms having revolute (R) and prismatic (P) pairs. Since all lower pairs are equivalent to some combination of R and P pairs, the method works for spatial mechanisms containing any lower pair. By using the method, spatial mechanisms are describable by simple equations which are easily programmable.

A new computational algorithm for 7R spatial mechanisms

1996 ◽  
Vol 31 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Blaise Morton ◽  
Michael Elgersma
Keyword(s):  
Computational Algorithm ◽  
Spatial Mechanisms

Computational Local Mobility Analysis of Mechanisms With Higher Kinematic Pairs

2016 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Computational Algorithm ◽  
Computational Approach ◽  
Computational Method ◽  
Canonical Coordinates ◽  
Mobility Analysis ◽  
Local Mobility ◽  
Lower Pair ◽  
Order Constraints ◽  
Algebraic Operations ◽  
Higher Kinematic Pairs

The finite mobility of a mechanism is reflected by its configuration space (c-space), and the mobility analysis aims at determining this c-space. Crucial for the computational mobility analysis is an adequate formulation of the constraints. For lower pair linkages an analytic formulation is the product-of-exponential (POE) formula in terms of the screw systems of the lower pair joints. In other words, the screw coordinates of a lower pair joint serve as canonical coordinates on the corresponding motion subgroup. For such linkages, a computational approach to the local mobility analysis has been reported recently. The approach is applicable to general multi-loop linkages. Higher pairs do not generate motion subgroups so that their motion cannot be expressed in terms of screw coordinates. Hence their kinematics cannot be expressed in terms of a POE, and there is no efficient and generally applicable computational method for the mobility analysis. In this paper a formulation of higher-order constraints for mechanisms with higher pair joints is proposed making use of the result for lower pair linkages. The method is applicable to mechanisms where each fundamental loop comprises no more than one higher pair, which covers the majority of mechanisms. Based on this, a computational algorithm is introduced that allows mobility determination. As for lower pair linkages, this algorithm only requires simple algebraic operations.

Mechanism Link Rotatability and Limit Position Analysis Using Polynomial Discriminants

1987 ◽  
Vol 109 (2) ◽  
pp. 178-182 ◽  
Author(s):  
R. L. Williams ◽  
C. F. Reinholtz
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Position Analysis ◽  
Numerical Example ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Limit Position

A theory is proposed for algebraically determining the limit positions of single-degree-of-freedom mechanisms. The absence of limit positions indicates that the link being considered is a fully rotating crank. This theory is applied in the present paper to the RSSR and RRSS spatial mechanisms. Conditions for spatial mechanisms analogous to Grashof’s law should be attainable using this theory. A numerical example is given to illustrate the theory.

scholarly journals The study of multiallelic genetic systems by matrix methods

1969 ◽  
Vol 14 (3) ◽  
pp. 167-183 ◽  
Author(s):  
C. Cannings
Keyword(s):  
Natural Selection ◽  
Autosomal Locus ◽  
Matrix Methods ◽  
Matrix Notation ◽  
Selection Processes ◽  
Special Cases ◽  
Large Populations ◽  
The Matrix ◽  
Random Segregation ◽  
Simple Equations

A matrix notation is developed to facilitate study of natural selection in large populations. The processes of mating (taking into account differences between genotypes in fertility in both sexes), segregation, and differential viabilities are each expressed in matrix notation. Assortative mating and non-random segregation can also be described by the method. The separate processes can then be combined to give simple equations relating the genic and genotypic frequencies in one generation to those in the previous generation. This will facilitate computer treatment of natural selection processes.The method can also be used to study equilibria and the conditions of their stability by examining the latents roots of the matrix. Several special cases of selection at an autosomal locus are examined. The method can be extended to sex-linked loci and two special cases are discussed.

Optimal Experimental Design With Nesting of Persons in Organizations

2013 ◽  
Vol 221 (3) ◽  
pp. 145-159 ◽  
Author(s):  
Gerard J. P. van Breukelen
Keyword(s):  
Repeated Measures ◽  
Optimal Number ◽  
Health Centers ◽  
Randomized Experiments ◽  
Optimal Sample ◽  
Treatment Conditions ◽  
Sampling Cost ◽  
Nested Designs ◽  
Simple Equations ◽  
Number Of Individuals

This paper introduces optimal design of randomized experiments where individuals are nested within organizations, such as schools, health centers, or companies. The focus is on nested designs with two levels (organization, individual) and two treatment conditions (treated, control), with treatment assignment to organizations, or to individuals within organizations. For each type of assignment, a multilevel model is first presented for the analysis of a quantitative dependent variable or outcome. Simple equations are then given for the optimal sample size per level (number of organizations, number of individuals) as a function of the sampling cost and outcome variance at each level, with realistic examples. Next, it is explained how the equations can be applied if the dependent variable is dichotomous, or if there are covariates in the model, or if the effects of two treatment factors are studied in a factorial nested design, or if the dependent variable is repeatedly measured. Designs with three levels of nesting and the optimal number of repeated measures are briefly discussed, and the paper ends with a short discussion of robust design.

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