Isomorphism (structural similarity) of kinematic chains (KCs) of mechanisms is an important issue in the structural synthesis, which must be identified to avoid the duplicate structures. Duplication causes incorrect family size, i.e., distinct KCs with a given number of links (n) and degree of freedom (dof). Besides simple joints kinematic chains (SJKCs), multiple joints kinematic chains (MJKCs) are also widely used because of their compact size and the methods dealing with such KCs are few. The proposed method deals with two different structural invariants, i.e., primary structural invariants (provide only the necessary condition of isomorphism), such as link connectivity number (LCN) of all the links, link connectivity number of chain (CCN), joint connectivity number (JCN) of all the joints, and joint connectivity number of chain (JCNC), and secondary structural invariants (provide the sufficient condition of isomorphism), such as power transmission (P) and transmission efficiency (T e ). Primary structural invariants are calculated using a new link–link connectivity matrix (LLCM), whereas secondary structural invariants are calculated using the concept of entropy of information theory. The method has been successfully tested for 10 and 11 links MJKCs (illustrative examples taken in the paper) and for the families of 18 MJKCs with 8 links, 2 MJs, 1-dof, and 3 independent loops; 22 MJKCs with 8 links, 1 MJ, 1-dof, and 3 independent loops; and 83 MJKCs with 9 links, 1 MJ, 2-dof, and 3 independent loops.

A new method is presented for the design of kinematotropic linkages based on 2-DOF kinematic chains that generate more than one surface. As an example of the proposed method, a kinematotropic linkage is obtained by studying a special case of the Bohemian dome which has two different parametrizations constructed by translation of circles and, therefore, two different hybrid kinematic chains can be designed to generate the same Bohemian dome. Each of these hybrid kinematic chains can generate two different surfaces and, thus, can be used in the proposed method. Parametrizations for the secondary surfaces are then obtained and studied. A total of 27 motion branches are found in the configuration space of this kinematotropic linkage. The singularities in the configuration space are further determined using the properties of the surfaces. The resultant linkage offers an explanation of Wholhart’s queer-square linkage other than its original paper folding. As part of the analysis of this example, the relationship between the properties of self-intersections in generated surfaces and the configuration space of the generator linkage is studied for the first time, leading to a description of motion branches related to self-intersections of generated surfaces.

The structural synthesis of Baranov trusses is still an open problem, although Baranov trusses are widely used in the design and analysis of mechanisms and robots. This paper proposes a systematic method for the structural synthesis of Baranov trusses. First, the definition review and the graph-form representations of Baranov trusses are proposed. Second, seven propositions on structural characteristics of Baranov trusses are concluded. Then, based on the set of constraint equations and a rigid subchain detection algorithm, a systematic method is presented to synthesize the complete set of Baranov trusses with a specified number of links. Finally, the synthesis results of contracted graphs (including valid and rigid contracted graphs) and topological graphs of Baranov trusses with up to 13 links are provided, and the synthesis methods and results between ours and the ones in the existing literature are compared and discussed in detail.

Planetary gear trains (PGTs) are widely used in transmission systems. The structural synthesis of PGTs is an effective way to create novel and excellent transmissions. In the structural synthesis of PGTs, the isomorphism detection (ID) is an essential and especially important process. The ID aims to avoid duplication and guarantee the uniqueness of each PGT. The reliability of the ID method directly determines the accuracy of the synthesis result. Unfortunately, when the existing ID methods are used to synthesize PGTs, the synthesis results are not consistent with each other. A very important reason is that the ID methods fail to work in some cases. This fact gives rise to the need of an extremely reliable ID method, which may resolve the contradiction in the existing synthesis results in the future. In this paper, our previous perimeter loop-based ID method, which is applicable for linkage kinematic chains and has been proved to be reliable and efficient, is improved to detect isomorphic PGTs. The improvements relative to our previous method are discussed in detail. The present method is fully automated with the aid of a computer program, and verified by the atlas of PGTs with up to six links, as well as some PGTs with seven, eight, and ten links.

Detection of isomorphism in planar and geared kinematic chains (GKCs) is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept “Net distance” is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains (PKCs) as well as GKCs. The proposed algorithm is applied on nine-link two-degrees-of-freedom (DOF) distinct kinematic chains completely and the results are presented. Algorithm is tested on examples from eight-link 1-DOF, ten-link 1-DOF, 12-link 1-DOF, and 15link 4-DOF PKCs. The algorithm is also tested on four-, six-link 1-DOF GKCs to detect isomorphism. All the results are in agreement with the existing literature.

The sketching of kinematic chains is important in the conceptual design of mechanisms. In general, the process of sketching kinematic chains can be divided into two steps, namely sketching topological graphs and converting them into the corresponding kinematic chains. This paper proposes a new method to automatically sketch topological graphs including both planar and nonplanar graphs. First, two parameters called moving sign (MS) and moving sign string (MSS) are defined, based on which a new algorithm is proposed to acquire all feasible layouts of the contracted graph by moving inner edges. All topological graphs synthesized from the same contracted graph are identified to have the shared feasible layouts, and another algorithm is proposed to determine the optimal layout for each topological graph. Then, topological graphs are sketched automatically by determining the location of vertices. The method has low complexity and is easy to be programmed using computer language.

An atlas of 98 microgrippers that recently appeared in Literature is herein presented by using four different forms: (a) a restyled layout of the original mechanical structure, (b) its corresponding pseudorigid body model (PRBM), (c) its kinematic chain, and finally, (d) its related graph. Homogeneity in functional sketching (a) is assumed to be greatly helpful to understand how these grippers work and what are the most significant differences between them. Therefore, a unified and systematic set of aesthetics and proportionality criteria have been adopted. Analogously, unified criteria for obtaining pseudorigid (b), kinematic (c), and graph (d) representations have been also used, which made the atlas easy to be read and inspected. The distinction among lumped and distributed compliance has been also accepted to develop the structure of the atlas. A companion paper has been prepared to present a survey on the variety of operational strategies that are used in these microgrippers.

A parallel mechanism possesses several advantages compared to a similar-sized serial mechanism, including the potential for higher accuracy and reduced moving mass, the latter enabling increased load capacity and higher acceleration. One of the most important issues affecting a parallel mechanism is the potential of parallel singularities. Such configurations strongly affect the performance of a parallel mechanism, both in the actual singularity and in its vicinity. For example, both the stiffness of a mechanism and the efficiency of the power transmission to the tool platform are related to the closeness to singular configurations. A mechanism with a mobility larger than the mobility of its tool platform is referred to as a kinematically redundant mechanism. It is well known that introducing kinematic redundancy enables a mechanism to avoid singular configurations. In this paper, three novel kinematically redundant planar parallel mechanisms are proposed. All three mechanisms provide planar translations of the tool platform in two degrees-of-freedom, in addition to infinite rotation of the platform around an axis normal to the plane of the translations. The unique feature of the proposed mechanisms is that, with the appropriate inverse kinematics solutions, all configurations in the entire workspace feature optimal singularity avoidance. It is demonstrated how it is sufficient to employ five actuators to achieve this purpose. In addition, it is shown how including more than five actuators significantly reduces the required actuator motions for identical motions of the tool platform, thereby reducing the cycle times for typical applications.

Robots designed for space applications, deep sea applications, handling of hazardous material and surgery should ideally be able to handle as many potential faults as possible. This paper provides novel indices for fault tolerance analysis of redundantly actuated parallel robots. Such robots have the potential for higher accuracy, improved stiffness, and higher acceleration compared to similar-sized serial robots. The faults considered are free-swinging joint failures (FSJFs), defined as a software or hardware fault, preventing the administration of actuator torque on a joint. However, for a large range of robots, the proposed indices are applicable also to faults corresponding to the disappearance of a kinematic chain, for example, a breakage. Most existing fault tolerance indices provide a ratio between a robot's performance after the fault and the performance before the fault. In contrast, the indices proposed in this paper provide absolute measures of a robot's performance under the worst-case faults. The proposed indices are based on two recently introduced metrics for motion/force transmission analysis of parallel robots. Their main advantage is their applicability to parallel robots with arbitrary degrees-of–freedom (DOF), along with their intuitive geometric interpretation. The feasibility of the proposed indices is demonstrated through application on a redundantly actuated planar parallel mechanism.

In this paper, we present a virtual chain approach for the mobility analysis of multiloop deployable mechanisms. First, the relative motion of the links of single-loop units in multiloop mechanisms are analyzed using the equivalent motion of certain types of open-loop virtual kinematic chains; these kinematic chains comprise some types of joints connected in series by flexible links. This reveals that the links in these virtual chains are not rigid when the mechanism is moving. The parameters of these virtual kinematic chains (such as the link length, the twist angle of two adjacent revolute joint axes, and so on) are variable. By using this approach that involves equivalent kinematic chains, the multiloop mechanisms can be considered equivalent to single-loop mechanisms with flexible links; the closure equations of such multiloop mechanisms can also be derived. The analytical procedures are explained using examples of multiloop mechanisms in which Myard mechanisms as used as the basic single-loop units. A prototype is also fabricated to demonstrate the feasibility of the proposed multiloop mechanism. The proposed method yields a more intuitive and straightforward insight into the mobility of complicated multiloop mechanisms.

If a part of a mechanism is restrained to rotate about a point not physically belonging to it, the mechanism is called a remote center-of-motion (RCM) mechanism. The RCM mechanisms are generally designed especially for robot-assisted minimally invasive surgery (MIS) systems, for which great progress has been made in recent years. An RCM mechanism type synthesis method is proposed in this paper by generalizing the intersection of motion planes. The existence of such motion planes is the fundamental feature of the classic Sarrus mechanism, for instance. The basic principle of the type synthesis method is to combine some typical planar mechanisms where their respective motion planes are free to tilt. Hence, the intersection line varies as the planes tilt. There is one invariant point on this intersection line, however, and this is the RCM point. The proposed method is used to design a class of spatial RCM mechanisms. And the kinematic characteristics of them are presented in this paper. In particular, several fully parallel two degree-of-freedom (DOF) RCM mechanisms and a 1-DOF RCM mechanism are considered in detail. Two spatial 3-DOF overconstrained RCM mechanisms are also obtained by the proposed method.

It is of great importance in the conceptual creative design of mechanical systems to synthesize as many feasible kinematic structures of mechanisms as possible. However, the methods for the structural synthesis of multiple joint kinematic chains are seldom addressed in literature even though they are widely used in various mechanical products. This paper proposes an automatic method to synthesize planar multiple joint kinematic chains. First, the bicolor topological graph and the bicolor contracted graph are introduced to represent the topological structures of multiple joint kinematic chains. Then, the characteristic number string of bicolor topological graphs is proposed and used to efficiently detect isomorphism in the synthesis progress. Finally, a systematic method for the synthesis of kinematic chains with one multiple joint is proposed, and the whole families of multiple joint kinematic chains with up to 16 links and all possible degrees of freedom are synthesized for the first time.

The creation of novel kinematic structures of mechanisms still represents a major challenge in the quest for developing new, innovative devices. In this setting, computer models that can automatically generate and visualize all possible independent structures in an intuitive manner prove to be valuable as a support in the creative process of the designer. This paper proposes an automatic approach for establishing the complete atlas database of 2-DOF kinematic chains and a systematic approach for the creative design of mechanisms based on such an atlas. First, the transformation of the kinematic structure into a graph-based representation is addressed. Then, an approach for the generation of all nonfractionated topological graphs of 2-DOF (degrees of freedom) kinematic chains using contracted graphs as well as a method for synthesizing all the fractionated topological graphs through the combination of corresponding 1-DOF kinematic chains are addressed. Based on these methods, the complete atlas database of 2-DOF kinematic chains up to 15 links is established in this paper for the first time. Using this complete database, a systematic approach for the creative design of mechanisms can be derived, as illustrated for the example of an 11-link 2-DOF rode tractor.

This paper attempts to establish unified topological models and corresponding mathematical representations for planar simple joint, multiple joint, and geared (cam) kinematic chains. First, the conventional topological representation models of kinematic chains are introduced. Then, new topological models of multiple joint and geared (cam) kinematic chains, which are derived from the topological model of simple joint kinematic chains, are presented. The characteristics of the new topological graphs and their associations with the topological graph of simple joint kinematic chains are also addressed. The most important merit of the new topological graphs is that it makes it much easier to undertake unified structure synthesis and further to establish conceptual design platform for various planar mechanisms. Synthesis examples of both multiple joint and geared chains are given, which show the effectiveness of the unified topological models.

This paper focuses on the synthesis of an independent suspension that can guide the wheel to track a straight line when moving up (jounce) and down (rebound). With displacement subgroups, it first synthesizes a rigid body guidance mechanism and verifies the result through screw theory. To simplify and optimize the loads of each kinematic chain of the knuckle, it investigates the static equations and ultimately synthesizes a symmetric redundant-constraint suspension structure, which could not only eliminate the shambling shocks induced by the jumping of wheels but also decrease the abrasion of tires. Theoretically, only one pair of noncoplanar kinematic chains is necessary to realize straight line guidance. However, a second pair of noncoplanar kinematic chains is particularly utilized to improve the load status of the links. Because of the redundant constraints induced by the suspension structures, the whole weight can be significantly reduced compared with the initial one. ADAMS simulations with a set of real parameters indicate that the rear suspension mechanism proposed in this paper can guide the wheel to follow a rectilinear locus during jounce and rebound. Therefore, this kind of independent suspension can improve the ride and handling properties of advanced vehicles.

The identification of link adjacency and joint incidence of kinematic chains and mechanisms is important and essential prior to the task of conceptual mechanism design. A careful observation method can be done in general; however, a computational approach is particularly needed for the design automation and algorithmic enumeration. This paper proposes a systematic approach for this goal in which a pseudogenetic concept is employed. The graph identification is then generalized from which the identifications of kinematic chains and mechanisms are automatically mapped. The illustrative examples show that the computation is simple and easily programmable. This development is helpful for the automated structural synthesis of mechanisms.

This paper proposes a synthesis method for rectilinear motion generating spatial mechanism with application to automotive suspension. First, it presents a generic process to synthesize the kinematic chains of a mechanism with the prescribed mobility, and then it deduces the construction criteria of feasible kinematic chains for such a mechanism. The most outstanding advantages of the rectilinear motion generating spatial mechanism used as the independent automotive suspension are that the orientation and position parameters such as kingpin, caster, camber, axis distance, and wheel track are always maintained constant during jounce and rebound. These ideal characteristics are guaranteed by the particular rigid guidance mechanism whose end effector only has one translation along an exact straight line.

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

A parallelogram-based 4 degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Schönflies motion that allows the end effector to translate in all directions and rotate around an axis parallel to a fixed direction. The theory of group of displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and an improved stiffness to the manipulator. This paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity, and the singularity analysis. Finally, a prototype of the manipulator, adding some considerations about its singularity-free design, and some technical applications in which the manipulator can be used are presented.