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This paper presents a novel tensegrity structure derived from the tensegrity triplex (also called the simplex or regular triangular prism) by using the linkage-truss transformation. In this paper, the tensegrity triplex is first transformed into a 6R linkage with vertical members as revolute joints and is coined the triplex linkage. With this, a novel 6R linkage was derived, whose joint axes are perpendicular to the joint axes of the triplex linkage and is coined the ortho-triplex linkage. Rigidity analysis based on screw theory demonstrates that both obtained linkages with infinitesimal mobility are prestress stable. Finally, transforming the ortho-triplex linkage to a truss, by using cables for tensional members and struts for compressional members, leads to a novel tensegrity that is coined ortho-triplex tensegrity. A non-dimensional quadratic form is further provided to analyze the sensitivity of prestress-stability in terms of the structural parameters. The process of derivation of this novel tensegrity presents a new way of designing tensegrity structures with prestress-stability analysis based on screw theory. [ABSTRACT FROM AUTHOR]

This paper explores essence of geometric constraints induced reconfiguration of single-loop kinematic chains with mobility one. Reconfigurable kinematic chains are firstly classified into four categories in light of variations of parameters in the Chebychev–Grübler–Kutzbach mobility criterion. Within these four categories, single-loop kinematic chains with mobility one but distinct motion branches are further classified in accordance with degeneration of degree-of-freedom of certain revolute joints. With the essence of reconfiguration, the interrelationship of motion-branch changes through constraint singularity induced transitory positions of reconfigurable single-loop linkages is revealed in the context of reciprocity of screws. Four basic geometric constraints leading to transitory positions are explored by analysing the Bennett plano-spherical linkage, a kinematic embodiment of Grassmann varieties. Geometric constraints induced screw-system variation and motion branch changes of a novel asymmetric 7R linkage and the line- and plane-symmetric Bricard 6R linkage with capability of reconfiguring their motion branches are subsequently analysed for interpreting the fundamentals explored. [ABSTRACT FROM AUTHOR]

• 3PRS parallel mechanisms are studied by finite displacement screw-based group method. • Manifold motions of mechanisms with different arrangements of R joints are expressed. • The finite and instantaneous motions of these mechanisms are modeled and compared. • How the limb arrangement affects the mechanism' motion is investigated and revealed. When limbs of a parallel mechanism have been selected, the geometric relation among limbs determines the mechanism's motion. The limb arrangement which affects the mechanism's motion raises a fundamental and significant issue. If a mechanism only owns limbs with Lie group motions, it is convenient to predict how a limb arrangement determines the mechanism's motion. However, if a mechanism is mainly or purely constituted by limbs with motions of general differential manifolds, it is difficult to find the influence of a limb arrangement. On this regard, this paper provides an in-depth investigation by focusing on motion analysis of parallel mechanisms consisting of three PRS limbs with planar-spherical manifolds. By formulating and comparing the motion characteristics of these mechanisms which though could be modeled difficultly by a mathematical tool without using the finite displacement screw, a finite displacement screw-based group method is proposed in this paper to resolve the raised issue. The novel approach presents results in expressions of new types of manifold motions, providing a foundation for design and application of parallel mechanisms having the various three-planar-spherical manifolds' intersection motions. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the geometry properties and certain restrictions of stroke induced by the special assemblage of a 3PUP parallel mechanism which consists of a fixed base, a platform and three limbs. The constraints exerted on the platform by a general PUP limb are analyzed based on screw theory. The disposition and analytical expression of all the constraints applied by three PUP limbs are revealed according to the geometry of the parallel mechanism and reciprocity of screws. Geometric-constraints induced bifurcation of the platform is analyzed and motion characteristics corresponding to each bifurcated motion branch and the transitory position of two bifurcated motion branches are derived corresponding to distinct restrictions of actuated strokes. The study further reveals the practical application of the 3PUP parallel mechanism in developing rehabilitation device for sprained subtalar joint. [Copyright &y& Elsevier]

Abstract: This paper presents a new metamorphic parallel mechanism that has the ability to change mobility in a wide range. Based on the newly invented reconfigurable Hooke joint with two distinct phases, the constraint forces are altered to be exerted on the platform. This change of constraint forces results in change of mobility of the mechanism and therefore degree of freedom of the platform. This paper applies screw system analysis, and by identifying both motion-screw system and constraint-screw system, the paper reveals six topological configurations with variable mobility. The particular phenomenon of bifurcated motion of the mechanism in its low-mobility configurations is further investigated based on constraint analysis. [ABSTRACT FROM AUTHOR]

The complex and articulated ball is one of the popular artifacts for collections and is highly expandable and collapsible. This paper investigates the mechanism structure of this magic ball by hypothetically decomposing the mechanism into kinematic loops and chains and subsequently into basic kinematic sub-chains, leading to the analysis of the mobility of the ball mechanism. Dismantling those kinematic chains which do not contribute to the mechanism mobility, the magic-ball mechanism is decomposed into a number of kinematic chains, and further disintegrated into two distinct types of elementary platforms with three and four legs respectively. The theory of the relationship of a screw system and its reciprocal system is then used to identify both common constraint and virtual constraint in each of the elementary platforms and to examine the mobility of those platforms. The analysis is then extended to the mobility analysis of the closed-loop circular kinematic chain and supplementary chains. A systematic analysis is hence produced in mechanism decomposition and in the analysis of virtual constraints. The paper produces a theoretical basis for the mobility analysis of the mechanism using mechanism decomposition and screw system analysis. [Copyright &y& Elsevier]

This paper presents a linear algebraic procedure in obtaining (6-n) reciprocal screws from an n-screw system of a robotic manipulator. The procedure starts by formulating the reciprocal relationship between a screw system and its reciprocal screw system in matrix form, and augmenting the screw matrix which is assembled with n screws in the screw system. Vectors of cofactors of the augmented row are then produced and the partitioning of the screw matrix is implemented to generate each of the (6-n) reciprocal screws. The theory developed in this paper provides a novel and simple procedure to obtain reciprocal screws from any screw system. The paper illustrates applications to cases with different screw systems. © 2003 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This paper proposes a new synthesis approach by using constraints for limb synthesis to target mobility-change in the mechanism construction. The limbs therefore produced have the facility to reconfigure the limb twist-system to change the screw system order for reconfigurability. This presents various reconfigurable limbs with geometric constraints of their joints based on the newly invented reconfigurable Hook (rT) joints. The procedure of the limb synthesis is put forward to fully utilize the property of the new joint for generating the reconfigurable limbs. The paper further presents a mobility-change condition to construct a metamorphic mechanism with the reconfigurable limbs. This gives a family of metamorphic parallel mechanisms that have the facility to change mobility in the range of 3– 6. A further family of metamorphic parallel mechanisms is proposed with a central strut. Their topological configuration change is investigated by examining the constraint change stemming from the phase alteration of the reconfigurable Hooke rT joint. [ABSTRACT FROM AUTHOR]

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input-output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism. [ABSTRACT FROM AUTHOR]

• Inspiration from line dependence of screws and their embodied geometry. • A novel reconfigurable spherical joint is presented based on linear dependence of screws. • Four phases of the rS joint are termed as source phase R, intermediate phase U, R s , and S. • Two novel metamorphic mechanism were obtained by inserting the rS joint. • Reconfiguration is revealed based on phase change of the rS joint and/or bifurcation. This paper presents a novel reconfigurable spherical (rS) joint resulting from the line dependence of screws and their embodiment geometry. Subsequently, the structure and phase change of the rS joint are elaborated. With this new invention, two novel metamorphic mechanisms, that are, the Schatz-derived metamorphic mechanism and the R(rS)R-R(rS)R metamorphic mechanism, are obtained by inserting the rS joint. The mechanisms entail a reconfiguration process that occurs in two manners: the phase change of the rS joint and the bifurcation of the mechanism. The Schatz-derived metamorphic mechanism entails reconfiguration by phase change of the rS joint and the bifurcation, the R(rS)R-R(rS)R metamorphic mechanism reconfigures the configuration based on phase change of the two rS joints. Remarkably, the former realizes the switch between two assembly configurations without resorting to disassembly and reassembly, and maintains the characteristics of the original Schatz mechanism while the rS joint situates in phase R. The latter changes the mobility and bridges gap between a spatial single-loop mechanism and a structure. With this new reconfigurable joint, various reconfigurable mechanisms could be generated by inserting the reconfigurable joint into the classical ones. [ABSTRACT FROM AUTHOR]

• A construction approach bridges origami and Bennett, Bricard linkages. • Kinematotropy of origami-inspired integrated 8R kinematotropic metamorphic mechanism. • The evolved overconstrained 6R and 4R linkages under peculiar geometrical constraints. • The kaleidocycle and deployable properties of this mechanism are illustrated. • It belongs to the intersection of kinematotropic linkages and metamorphic mechanisms. Origami engineering as an interdisciplinary subject brings thriving progress of mechanisms innovation. In this paper, a construction approach from origami to multiple spherical-integrated mechanisms is proposed and subtly sets up the bridge between origami and Bennett linkage, Bricard linkage. Subsequently, the attention is drawn to a special origami-inspired integrated 8R kinematotropic metamorphic mechanism. The paper applies screw theory to illustrating the reconfigurability of singular configurations with distinct parametric constraints in the 8R mechanism. Two overconstrained linkages, a 4R linkage and a 6R linkage, are evolved under peculiar geometrical constraints respectively. Furthermore, the kaleidocycle and deployable properties of the 8R mechanism are revealed. The paper hence not only presents an interesting work extracted from origami but also sheds light on the promising investigation about the intersection of distinct types of reconfigurable mechanisms. Finally, by using the kinematotropic metamorphic 8R mechanism as the reconfigurable trunk, a novel quadruped robot is built and its characteristics will be investigated in future research. [ABSTRACT FROM AUTHOR]

The furcation point in a mechanism is a salient feature of reconfigurable mechanisms and change of a joint from an unconstrained condition to a geometrically constrained condition resulting in naturally link annexing with this geometrical constraint is a typical feature of metamorphic mechanisms. This paper presents a novel 6R metamorphic mechanism by inserting two revolute joints to a Bennett mechanism. From parameters of this novel 6R metamorphic mechanism, the source mechanism before changing is a special case of the Bricard 6R line-symmetric mechanism while the closure equation gives constraint conditions of joints. The geometrically constrained conditions result in variable motion branches of the mechanism. When all joints are unconstrained geometrically, two 6R motion branches can be obtained and when two joints are under geometric constrained, three 4R motion branches can be obtained. Further, three further motion branches with coaxial joints are obtained and motion branch transformation is illustrated with kinematic curves. For each of the motion branches, motion screws of this novel 6R metamorphic mechanism present corresponding geometry morphology and are analysed with screw algebra. [ABSTRACT FROM AUTHOR]

It has been a desire to unify the models for structural and parametric analyses and design in the field of robotic mechanisms. This requires a mathematical tool that enables analytical description, formulation and operation possible for both finite and instantaneous motions. This paper presents a method to investigate the algebraic structures of finite screws represented in a quasi-vector form and instantaneous screws represented in a vector form. By revisiting algebraic operations of screw compositions, this paper examines associativity and derivative properties of the screw triangle product of finite screws and produces a vigorous proof that a derivative of a screw triangle product can be expressed as a linear combination of instantaneous screws. It is proved that the entire set of finite screws forms an algebraic structure as Lie group under the screw triangle product and its time derivative at the initial pose forms the corresponding Lie algebra under the screw cross product, allowing the algebraic structures of finite screws in quasi-vector form and instantaneous screws in vector form to be revealed. [ABSTRACT FROM AUTHOR]

• The generalized Jacobian analysis at both limb and platform levels were formulated. • The multilevel Jacobian contains full constraint, kinematics, and statics information. • A unified approach for the determination of unknown twists and wrenches was proposed. • An approach for the construction of repelling screw system was formulated. • The influence of the linear combination of screws on repelling screws was revealed. This paper presents a unified and generalized approach for the construction of Jacobian matrices for general, nonredundant parallel manipulators that possess serial and/or mixed-topology limbs. Using linear algebra, a method for the calculation of repelling screws is proposed, based upon which the underlying correlations amongst the screws (twists and wrenches) that correspond to both the permitted, and constrained, motions of general mechanisms are identified and analyzed. The effect of linear combinations on the repelling screw system is revealed, and further used to determine the constraint wrenches/twists of a parallel manipulator and its limbs. By means of utilising repelling screws, the dualities in parallel and serial mechanisms are revisited and extended. Furthermore, a simple and unified method for the identification of unknown twists and wrenches is proposed, based upon which an intuitive and systematic approach for the formulation of generalized Jacobian matrices for nonredundant parallel manipulators is derived. The generalized multilevel hierarchical Jacobian contains complete constraint, singularity, kinematics, and statics information at both limb and platform levels. A number of provided examples demonstrate the effectiveness and application of the proposed approach. [ABSTRACT FROM AUTHOR]

• Repelling screws are proposed to elaborate the dualities of compliant mechanisms. • A method for the construction of the repelling screw system is proposed. • An approach to transform between parallel and serial compliant mechanisms is proposed. • Two methods to adjust the configuration of compliant parallel mechanism are proposed. • The orthogonal and dual correlations among the twist/wrench subspaces are formulated. This paper provides a geometrical insight into the dualities of compliant mechanisms via repelling screws. A method for the construction of the repelling screw system is proposed. By means of screw theory and linear algebra, the closed-loop relationships among the twist/wrench spaces of both actuation- and constraint-screw systems are identified, upon which the kinematics, statics and stiffness/compliance of both full- and limited-mobility compliant mechanisms are analysed. The internal correlations between repelling screws and dualities of mechanisms are investigated, which reveals both orthogonal and dual properties of mechanisms with either parallel or serial configuration. The repelling-screw-based representation is applied to describing the permitted motions and restricted constraints of the mechanism. In addition, a novel and systematic approach for parallel-to-serial/serial-to-parallel transformation is proposed, which retains the capability of changing the constraints and relative dimensions of the target configuration to better suit a specific task. A few examples conducted demonstrate the feasibility of the proposed approach and the effectiveness of the repelling-screw based interpretations of mechanism geometries. [ABSTRACT FROM AUTHOR]