Structural Enumeration of Cam-Modulated Linkages

The structural synthesis of Baranov trusses is an open problem even though it finds its wide usage in design and analysis of mechanisms and robotics. A Baranov truss is a planar zero DOF kinematic chain, which contains no rigid subchains. The present work aims at synthesising the complete collection of N - link Baranov trusses by adding a binary link to (N – 1) - link, 1 degree of freedom (DoF) simple jointed kinematic chains. From this collection, chains which contain degenerate sub-chains are identified and removed as they are not Baranov truss by definition. Next, an isomorphism test is carried out to identify distinct chains and resulting complete collection of N-link Baranov trusses is reported.

In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains

This paper deals with the development of a standard code for the unique representation of pin-jointed kinematic chains based on graph theory. Salient features of this method include the development of an efficient and robust algorithm for the identification of isomorphism in kinematic chains; the formulation of a unified procedure for the analysis of symmetry in kinematic chains; and the utilization of symmetry in the coding process resulting in the unique well-arranged numbering of the links. This method is not restricted to simple jointed kinematic chains only, and it can be applied to any kinematic chain which can be represented as simple graphs including open jointed and multiple jointed chains. In addition, the method is decodable as the original chain can be reconstructed unambiguously from the code values associated with the chains.

A computerized methodology for structural synthesis of kinematic chains: Part 1— Formulation

A new matrix, called the joint-joint relation matrix, is defined for representing the structure of a kinematic chain. An algorithm has been developed for deriving the joint-joint distance matrix of a kinematic chain from its joint-joint relation matrix with the help of the computer. A new structural invariant, called the Arranged Sequence of Total Distance Ranks of all the Joints, and based on the concept of distance, has been developed for a kinematic chain, leading to the development of a simple methodology for detecting isomorphism among planar kinematic chains with simple joints.

A new atlas for 8-bar kinematic chains with up to 3 prismatic pairs using Joint Sorting Code

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.

In a kinematic chain, the links are connected to each other through joints. The connectivity of a joint indicates the number of joints to which it is connected. The connectivity level of a joint indicates the distance by which it is separated from the adjacent joints. The concept of joint connectivity and its application to detect isomorphism among kinematic chains and their inversions has been already reported by authors. The method utilizes the connectivity of joints at different levels to detect isomorphism and inversions among planar kinematic chains. The method is applied to eight-, nine-, and ten-link planar kinematic chains. The results so obtained are in agreement with those available in the literature. In this study, the method is further improved by incorporating the type of joint to make it more effective for the detection of isomorphism and distinct inversions. A joint connectivity table completely representing the kinematic chain is proposed. The application of the method is extended for the determination of additional topological characteristics of chains such as categorization of kinematic chains and selection of preferred frame, input and output links for function and path generation. The concept of ‘Motion Transfer Ability’ is introduced and utilized to develop numerical measures for comparing and categorizing the chains at the synthesis stage of mechanism design for a specific application. The method was successfully tested on planar kinematic chains with single and multiple degrees of freedom and the results for eight- and nine-link kinematic chains are appended.

Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

In this paper, a new method is proposed for structural synthesis of planar closed kinematic chains with all the possible kinds of multiple joints according to given number K-independent loops up to maximum multiple joint factor Vmax(K). At first, the new procedure for structural synthesis of non-fractionated and fractionated multiple joint kinematic chains based on the combination of corresponding simple and multiple joints is presented. Then the atlas database with all the possible kinds of multiple joints containing various 24 (case K = 4) multiple joint non-fractionated and fractionated structures is established and illustrated. Next, all the possible multiple joint assortments ([M.J.A.]) for non-fractionated as well as fractionated 10-link 1-DOF multiple joint kinematic chains with up to pentagonal links with K = 4 and up to Vmax = 6 are synthesized and separated for the first time. Finally, the complete structural analysis of multiple joint kinematic chains for industrial application in 10-link manipulators designed from the atlas of synthesized multiple joint kinematic chains is conducted.

Creative design of a wheel damping mechanism

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.

This chapter introduces an original theory of loop algebra and its application in isomorphism identification, rigid sub-chain detection, and atlas database of kinematic chains. Introduced first is the unified topology modeling of planar kinematic chains with simple joints, multiple joints, and geared (cam) joints. Based on the array representation of loops in the topological graphs of kinematic chains, basic loop operations are introduced, and the loop algebra is established. The most important problem of isomorphism identification in the automatic structural synthesis of kinematic chains is presented by finding a unique representation of topological graphs. Finally, the digital atlas database for the topological graphs of kinematic chains is also provided.

This review article provides a comprehensive overview and classification of the joint types used in the steerable tips of minimally invasive surgical instruments. The review was carried out with the objective to pinpoint the essence of the joints' fundamental mechanical design and to provide a qualitative comparison of their strengths and weaknesses with respect to a number of straightforward criteria. Besides researching the ASME scientific literature, the entire Espacenet patent database was searched using the keywords endo* or lapar* or surg* in title and steer* or articu* or deflect* in title or abstract. The extensive scope of the patent results was further limited to World (WO), United States (US), and European (EP) patents only as well as to the period of the last decade, 2003–2013, with a few exceptions predating this period. Overall, more than 840 patents were reviewed and categorized on the basis of the joints' mechanical design and supplemented with the scientific papers. A number of joint categories and subcategories were identified. At the fundamental level the joints can be differentiated as planar and spatial, where the spatial are further split as perpendicular mirrored and revolved. Based on the means of establishing rotational motion, the joint types can be discriminated as rolling, sliding, the combination of rolling and sliding, and bending. Lastly, the rolling and sliding categories can be further split with regard to the phenomenon or feature used for transferring the rotational motion, i.e., friction, teeth, belts, curved features, and hinges. In general, the most favored joint types were identified as the sliding and the bending joint categories overall. Nevertheless, it was recognized that no single fundamental joint type can be considered as ideal and that novel and preferably more superior joint configurations can be generated by combining several fundamental categories together.

In intelligent mechanism design, isomorphism identification of mechanism kinematic chains (IIMKC) is aimed at avoiding repeated mechanism design and is proved to be an NP-complete problem. In this paper, kinematic chains are represented by graphs. An improved hybrid immune algorithm, which integrates the clonal selection immune algorithm with genetic algorithm and the local search algorithm, is proposed to solve IIMKC problem. Moreover, the novel saving and updating operator is proposed to save the best antibodies and maintain a diverse repertoire of antibodies for improving performance of clonal selection. In addition, the pseudo-crossover operator is introduced to enhance the efficiency of genetic algorithm. Simulation results validate the high efficiency and robustness of the hybrid immune algorithm.