Jian S. Dai

Mobility of Overconstrained Parallel Mechanisms

The Kutzbach-Grubler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Matrix Representation of Topological Changes in Metamorphic Mechanisms

Metamorphic mechanisms form a class of mechanisms that has the facilities to change configuration from one kind to another with a resultant change in the number of effective links and mobility of movement. This paper develops formal matrix operations to describe the distinct topology of configurations found in a metamorphic mechanism and to complete transformation between them. A new way is hence introduced for modeling topological changes of metamorphic mechanisms in general. It introduces a new elimination E-elementary matrix together with a U-elementary matrix to form an EU-elementary matrix operation to produce the configuration transformation. The use of these matrix operations is demonstrated in both spherical and spatial metamorphic mechanisms, the mechanistic models taken from the industrial packaging operations of carton folding manipulation that stimulated this study.

Interrelationship between screw systems and corresponding reciprocal systems and applications

This paper discusses the relationship between a screw system and its corresponding reciprocal system based upon set theory, proposes a theorem, makes a proposition with corollaries to specify the relationship between the two screw systems and characterises all cases in screw systems. The theory is then applied to the one-, two-, and three-systems and their corresponding reciprocal five-, four-and three-systems, and used to predict reciprocal screws and the subsequent relationship with the existing screw system. A further application is given by selecting screws to design a system such that a certain intersection is desirable between the system and its reciprocal system. As a result, a method of generating a one-system of reciprocal screw from a five-system and of generating a reciprocal system from a co-reciprocal system is given.

Null–space construction using cofactors from a screw–algebra context

This paper develops an approach for constructing the null space N(A) of a linear system of homogeneous equations using the cofactors of an augmented coefficient matrix A. The relationship between the row space R(AT) and null space is exploited by introducing an augmenting vector which is linearly independent of the row space and dependent on the null space. The resultant null space is shown to be a vector of cofactors of the augmenting row of the coefficient matrix and is invariant. This provides a straightforward solution to a linear system of homogeneous equations without going through Gauss-Seidel elimination. The approach is derived from a onedimensional null space and is extended to a multidimensional one by partitioning the coefficient matrix and consequently constructing a set of (n−m) null–space vectors based on cofactors. Examples are given and accuracy is compared with Gauss–Seidel elimination. The approach is further used in a screw–algebra context with a simple procedure to obtain a system of reciprocal screws representing a set of constraint wrenches from a set of twists of freedom, in the form of a linear system of homogeneous equations in R6. The paper provides rigorous proofs and applications in both linear algebra and advanced kinematics.

A High-performance Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation

In this paper we present a redundantly actuated parallel mechanism for ankle rehabilitation. The proposed device has the advantage of mechanical and kinematic simplicity when compared with the state-of-the-art multi-degree-of-freedom parallel mechanism prototypes while at the same time it is fully capable of carrying out the exercises required by the ankle rehabilitation protocols. Optimization of the device workspace, dexterity, torque output and size was carried out during the design phase of the device. The development of the system involved the realization of a new customized linear actuator able to meet the speed and force requirements of the device functionality. We also discuss the impedance-based control scheme used for the redundantly actuated device, which allows the execution of both assistive and resistive strengthening rehabilitation regimes. Results from the control of a single linear actuator and further experimental tests including the position tracking of the fully actuated platform are presented. It is believed that the performance and the simplicity of the proposed mechanism will allow the widespread use of the system as a new aid tool for ankle rehabilitation.

Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism

This paper presents a metamorphic kinematic pair extracted from origami folds in the context of mechanisms, its evolved metamorphic chain, and the novel metamorphic parallel mechanism. This paper starts from the generic issues of topological representation for metamorphic mechanism, leading to unified elementary matrix operation for presentation of topological variation. Phase matrix and augmented adjacency matrix are developed to present the topological state and geometry of metamorphic mechanism in an evolutionary process. The metamorphic kinematic pair has the ability of changing mobility to generate different motion patterns based on mobility change correlated with the link annex induced topological phase change. This paper then investigates topological variation of the metamorphic chain and the topological subphases are enumerated in accordance with structure evolution. Using the metamorphic chain as chain-legs, a multiloop metamorphic mechanism with ability of performing phase change and orientation switch is constructed. The disposition of constraints and geometric constraints induced bifurcated motion are analyzed based on screw theory. The topological variation of the metamorphic parallel mechanism is addressed and the foldability is verified by physical device.

Mobility Change in Two Types of Metamorphic Parallel Mechanisms

This paper presents a new joint coined as the rT joint and proposes two types of metamorphic parallel mechanisms assembled with this rT joint. In the first type, the mechanism changes its topology by turning the rT joints in all limbs into different configurations. This change in mobility is completed by two cases illustrated by a 3(rT)PS metamorphic parallel mechanism having variable mobility from 3 to 6 and a 3(rT)P(rT) parallel mechanism having various configurations including pure translations, pure rotations, and mobility 4. In the second type, a central strut with the rT joint is added in a parallel mechanism. The variable mobility of the mechanism results from the topological change of the central (rT)P(rT) strut. This is illustrated in a 3SPS-1 (rT)P(rT) metamorphic parallel mechanism, which changes its mobility from 4 to 5. It is demonstrated in mobility analysis that the change in local mobility of each limb results in the change in the platform mobility that a metamorphic process can be achieved. This particular analysis leads to advancement of improved Grubler-Kutzbach criterion by introducing the local mobility factor in the mobility analysis.

Orientation and Workspace Analysis of the Multifingered Metamorphic Hand—Metahand

This paper introduces for the first time a metamorphic palm and presents a novel multifingered hand, known as Matahand, with a foldable and flexible palm that makes the hand adaptable and reconfigurable. The orientation and pose of the new robotic hand are enhanced by additional motion of the palm, and workspace of the robotic fingers is complemented with the palm motion. To analyze this enhanced workspace, this paper introduces finger-orientation planes to relate the finger orientation to palm various configurations. Normals of these orientation planes are used to construct a Gauss map. Adding an additional dimension, a 4-D ruled surface is generated to illustrate orientation and pose change of the hand, and an orientation-pose manifold is developed from the orientation-pose ruled surface. The orientation and workspace analysis are further developed by introducing a triangular palm workspace that evolves into a helical surface and is further developed into a 4-D representation. Simulations are presented to illustrate the characteristics of this new dexterous hand.

A six-component contact force measurement device based on the Stewart platform

Abstract This paper describes the design of a six-component contact force measuring device, the purpose of which is to verify a system of theories that predict the forces found in robotic grasping. The geometry of the device is based upon that of the Stewart platform manipulator, configured symmetrically. The elastic properties of the device as a whole, and of its legs, are analysed and chosen so that the device possesses appropriate characteristics. The resulting design is described, and its calibration and use are reported. Particular attention is paid to the synthesis of the elastic properties of the system, including an elastic central strut to maintain tension in the legs, which themselves are designed for acceptable sensitivity. The whole device is shown to give good results in contact force measurements.

Biological Modeling and Evolution Based Synthesis of Metamorphic Mechanisms

A methodology for synthesis and configuration design of metamorphic mechanisms is developed in this paper based on biological modeling and genetic evolution with biological building blocks. The goal is to conceive an appropriate source-metamorphic-mechanism configuration when the multiple phases of kinematic functions are given. The key enabler is the way of developing genetic evolution in modeling and design by capturing the metamorphic configuration characteristics. With the unique characteristic of achieving multiple working-phase functions in a mechanism, the metamorphic mechanism possesses two features: one, the ametabolic feature referring to the specified working phases that can be accomplished by a number of traditional mechanisms; two, the metamorphic feature occurring in transition between different working phases, resulting in change of topology of the mechanism. Based on this transition between phases, the concept of mechanism evolution is for the first time introduced in this paper based on biological building blocks in the form of metamorphic cells and associated intrinsic elements as the metamorphic gene. This leads to development of cell evolution and genetic aggregation with mechanism decomposition and evolutionary operation based on mapping from the source-metamorphic mechanism to multiphase working configurations. Examples are given to demonstrate the concept and principles.