Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: Application to 12- and 14-bar single degree-of-freedom chains

2005 ◽  
Vol 40 (9) ◽  
pp. 1030-1050 ◽  
Author(s):  
Eric A. Butcher ◽  
Chris Hartman
Keyword(s):  
Hierarchical Classification ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree

scholarly journals On rigid origami II: quadrilateral creased papers

2020 ◽  
Vol 476 (2237) ◽  
pp. 20200020
Author(s):  
Zeyuan He ◽  
Simon D. Guest
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Quadrilateral Meshes ◽  
Single Degree ◽  
Potential Applications

Miura-ori is well known for its capability of flatly folding a sheet of paper through a tessellated crease pattern made of repeating parallelograms. Many potential applications have been based on the Miura-ori and its primary variations. Here, we are considering how to generalize the Miura-ori: what is the collection of rigid-foldable creased papers with a similar quadrilateral crease pattern as the Miura-ori? This paper reports some progress. We find some new variations of Miura-ori with less symmetry than the known rigid-foldable quadrilateral meshes. They are not necessarily developable or flat-foldable, and still only have single degree of freedom in their rigid folding motion. This article presents a classification of the new variations we discovered and explains the methods in detail.

Detection of Improper General Spatial Kinematic Chains With Different Types of Pairs

1994 ◽  
Author(s):  
Xian-Wen Kong ◽  
Ting-Li Yang
Keyword(s):  
Unsolved Problem ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Different Types ◽  
Necessary And Sufficient ◽  
Topological Synthesis

Abstract Improper general spatial kinematic chains (GSKCs) due to the effect of pair types may be generated during the process of topological synthesis of GSKCs with different types of pairs. Thus, detection of improper GSKCs is necessary in topological synthesis of GSKCs with different types of pairs. Unfortunately, it is still an unsolved problem. In this paper, a method for detecting improper GSKCs is presented. Both a necessary and sufficient condition and a sufficient condition for proper GSKCs with R, P, H, T and C pairs are introduced at first. Based on these two conditions, an algorithm to detect improper GSKCs is then developed which is very efficient and suitable for topological synthesis of GSKCs with R, P, H, T and C pairs. The proposed algorithm has been applied to topological synthesis of 1- and 2-loop, single degree of freedom GSKCs with R, P, H, T and C pairs and the corresponding atlas is obtained.

On the Flexibility of Spatial Kinematic Chains

1986 ◽  
Vol 10 (4) ◽  
pp. 213-218
Author(s):  
A.C. Rao
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Arrangement ◽  
Kinematic Chains ◽  
Single Degree ◽  
A Chain ◽  
Space Mechanisms

A number of distinct or non-isomorphic kinematic chains exist for a specified number of links and joints. For example, sixteen distinct chains can be obtained with eight links and two hundred and thirty chains with ten links having a single degree of freedom. Similarly, many space mechanisms can be formed with four links and joints having different degrees of freedom. So far no measure is available to know which of these possesses greater mobility or flexibility. Flexibility is not to be confused with the degree of freedom. Intuitively one feels that a six-link chain has greater flexibility than a four-bar chain both having the same degrees of freedom. Though the mobility of a chain increases with the number of links one is not sure how the structural arrangement, type of links and joints, their numbers and sequence etc. influence the same. Combining graph theory with the concepts of probability, simple formulae are developed to investigate the relative merits of spatial and planar kinematic chains. The greater the flexibility or mobility of the chain, the higher is the ability to meet the motion requirements, i.e., a chain having greater entropy can be expected, say, to reproduce a given function more accurately.

Classification of Periodic Solutions in a Single-Degree-of-Freedom System With Backlash

2007 ◽  
Author(s):  
Bart Besselink ◽  
Amit Shukla ◽  
Rob Fey ◽  
Henk Nijmeijer
Keyword(s):  
Piecewise Linear ◽  
Continuation Method ◽  
Degree Of Freedom ◽  
Multiple Shooting ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Boundary Crossings ◽  
Single Degree ◽  
Piecewise Linear System

In this paper a single degree-of-freedom system with backlash is studied for its periodic response. This system is modeled as a piecewise linear system with discontinuity in the net restoring force, caused by additional damping in the contact-zone. The periodic orbits are classified by their number of subspace boundary crossings and Floquet multipliers. For this classification, the known analytical solutions in the different subspaces are used in the multiple shooting algorithm and a continuation method. Some observations are also presented about the qualitative features (such as symmetry, rigid body solutions) exhibited by this class of systems.

Study of Dead-Centre Positions of Single-Degree-of-Freedom Planar Linkages Using Assur Kinematic Chains

2006 ◽  
Vol 220 (7) ◽  
pp. 1057-1074 ◽  
Author(s):  
G R Pennock ◽  
G M Kamthe
Keyword(s):  
Direct Application ◽  
Degree Of Freedom ◽  
Special Structure ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Original Technique ◽  
Stationary Configuration ◽  
Planar Linkages ◽  
Dead Centre

The article presents an original technique, using the concept of Assur kinematic chains (AKCs), to determine whether a single-degree-of-freedom planar linkage is in a dead-centre position, i.e. a position where the input link is instantaneously stationary. An AKC is a special structure with mobility zero from which it is not possible to obtain a simpler substructure of the same mobility by removing one or more links. The article presents the concept of modularization of planar linkages into AKC based on the choice of the input link. Then, the article presents the constraints on the locations of the instantaneous centres of zero velocity (or instant centres) for a single-degree-of-freedom planar linkage to be in a stationary configuration, i.e. a configuration where one, or more, of the links is instantaneously stationary. The article shows that constraints on the locations of the instant centres for a stationary configuration are satisfied if an AKC, as part of the linkage, gains a degree of freedom. As the modularization of a planar linkage is based on the choice of the input link, the stationary configurations, determined by this method, are in fact dead-centre positions. Finally, this method is applied to indeterminate linkages, i.e. a class of single-degree-of-freedom planar linkages for which it is not possible to locate all the secondary (or unknown) instant centres by the direct application of the Aronhold—Kennedy theorem.

Split Hamming String as an Isomorphism Test for One Degree-of-Freedom Planar Simple-Jointed Kinematic Chains Containing Sliders

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Varadaraju Dharanipragada ◽  
Mohankumar Chintada
Keyword(s):  
Adjacency Matrix ◽  
Visual Inspection ◽  
Degree Of Freedom ◽  
Simple Test ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Starting Point ◽  
Prismatic Joints ◽  
In Parenthesis

Over the last six decades, kinematicians have devised many tests for the identification of isomorphism among kinematic chains (KCs) with revolute pairs. But when it comes to KCs with prismatic pairs, tests are woefully absent and the age-old method of visual inspection is being resorted to even today. This void is all the more conspicuous because sliders are present in all kinds of machinery like quick-return motion mechanism, Davis steering gear, trench hoe, etc. The reason for this unfortunate avoidance is the difficulty in discriminating between sliding and revolute pairs in the link–link adjacency matrix, a popular starting point for many methods. This paper attempts to overcome this obstacle by (i) using joint–joint adjacency, (ii) labeling the revolute pairs first, followed by the sliding pairs, and (iii) observing whether an element of the adjacency matrix belongs to revolute–revolute (RR), revolute–prismatic (RP) (or PR), or prismatic–prismatic (PP) zone, where R and P stand for revolute and prismatic joints, respectively. A procedure similar to hamming number technique is applied on the adjacency matrix but each hamming number is now split into three components, so as to yield the split hamming string (SHS). It is proposed in this paper that the SHS is a reliable and simple test for isomorphism among KCs with prismatic pairs. Using a computer program in python, this method has been applied successfully on a single degree-of-freedom (DOF) simple-jointed planar six-bar chains (up to all possible seven prismatic pairs) and eight-bar KCs (up to all ten prismatic pairs). For six-bar chains, the total number of distinct chains obtained was 94 with 47 each for Watt and Stephenson lineages. For eight-bar chains, the total number is 7167 with the distinct chain count and the corresponding link assortment in parenthesis as 3780(0-4-4), 3037(1-2-5), and 350(2-0-6). Placing all these distinct KCs in a descending order based on SHS can substantially simplify communication during referencing, storing, and retrieving.

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