Metamorphic Parallel Mechanism Research Articles

Unified Singularity Crossing of a 3-(rR)PS Metamorphic Parallel Mechanism through Dynamic Modeling

Metamorphic parallel mechanisms can change into multiple configurations with different motion types and mobility, which consequently yield different solutions of inverse dynamics when crossing singularity. Thus, a unified solution of inverse dynamics to cross singularity becomes important. This solution relies on the consistency condition, the first indeterminate form, and this paper proposes an additional condition by extending into the second indeterminate form. This paper presents unified dynamic models of a 3-(rR)PS metamorphic parallel mechanism to pass through singularities. The analysis is carried out on all three configurations of the 3-(rR)PS metamorphic parallel mechanism. The dynamic models are established using Lagrange formulation, and three conditions to cross singularities are employed. The first condition is based on the consistency condition where the uncontrollable motion should be reciprocal to the wrench matrix. The denominator of inverse Jacobian is its determinant whose value is zero at singularities. This singularity can be discarded by compensating the numerator to be zero. Both the numerator and denominator are null, and this indeterminate form becomes the second condition. Both conditions are sufficient for inverse dynamics of one configuration to pass through singularity, but not for other configurations. Therefore, the second indeterminate form is proposed to be the third condition to be fulfilled. Consequently, the 11th-degree polynomial is required for path planning. The results are presented and confirmed by ADAMS simulation.

Kinematic Analysis and Workspace Investigation of Novel 3-RPS/(H) Metamorphic Parallel Mechanism

Abstract 3-RPS/(H) Metamorphic parallel mechanism based on conventional mechanisms is proposed in this study. In contrast to the 3-RPS mechanism, the 3-RPS/(H) mechanism comprises a novel intermediate metamorphic limb. The different constraints provided by the intermediate metamorphic limb and locking device enhance the dexterity of the metamorphic parallel mechanism. The configurations of the 3-RPS/(H) metamorphic parallel mechanism are analyzed and their degrees-of-freedom are obtained. Additionally, an inverse kinematic analysis of the mechanism is performed, and its workspace is compared with that of a conventional 3-RPS parallel mechanism with similar parameters. The results demonstrate that the 3-RPS/(H) metamorphic parallel mechanism exhibits better dexterity than that of the 3-RPS mechanism. Moreover, the effects of different structural parameters of the metamorphic parallel mechanism on the workspace are analyzed. Finally, the singularity analysis of the mechanism is performed. The results provide a theoretical basis for the design and optimization of mechanical legs.

A New Metamorphic Parallel Leg Mechanism with Reconfigurable Moving Platform

This paper proposes the concept of full configuration state of metamorphic mechanism. Based on the concept, the configuration synthesis principle of metamorphic parallel mechanism is put forward. Firstly, a metamorphic parallel mechanism in full configuration state is synthesized, and then full configuration state evolves into a specific configuration state by increasing constraints or decreasing degrees of freedom. A reconfigurable moving platform based on the triple symmetric Bricard spatial closed-loop mechanism with a single degree of freedom is proposed. Based on this, a new method for switching motion configuration states of the metamorphic parallel mechanism is constructed. According to the configuration synthesis principle presented above, a novel metamorphic parallel mechanism that can switch between three- and four-degree-of-freedom is synthesized, and then the triple symmetric Bricard spatial closed-loop mechanism is used as the reconfigurable moving platform (that is, the reconfigurable foot of a walking robot) of the metamorphic mechanism, and thus, a novel metamorphic parallel leg mechanism is created. The screw theory is used to verify the degrees of freedom of the new type of metamorphic parallel leg. The proposed metamorphic parallel leg mechanism is expected to improve flexibility and adaptability of walking robots in unstructured environment.

Kinematic analysis of a novel 2-PrRS-PR(P)S metamorphic parallel mechanism

Lower mobility parallel mechanisms have been developed in different structures and widely applied in industry, but still have disadvantages in various tasks and functional requirements. A 2-PrRS-PR(P)S metamorphic parallel mechanism with two working configurations and a transiting configuration is presented. First, the architecture and the way of metamorphosis about the mechanism are described in detail. The mobility of the metamorphic parallel mechanism is obtained with screw theory. Furthermore, the parasitic motions in different configurations are derived based on the geometry constraint conditions. Both the inverse kinematic problem and forward kinematic problem of the mechanism are investigated by the closed-loop equation and validated via numerical examples. Then, the velocity and acceleration in two working configurations are obtained by the derivation of the inverse kinematic problem. Finally, the reachable orientation workspaces are discussed using the three-dimensional search method in different configurations. A comparison with the 3-PRS PM without metamorphic mechanism in workspace is presented and an example of the metamorphic parallel mechanism in robotic supporting leg is presented. The above analyses provide theoretical foundations for application of this mechanism.

Reconfiguration of a 3-(rR)PS Metamorphic Parallel Mechanism Based on Complete Workspace and Operation Mode Analysis

Abstract This paper focuses on the reconfiguration of a 3-(rR)PS metamorphic parallel mechanism based on complete workspace and operation mode analysis. The mechanism consists of three (rR)PS legs, and each (rR) joint is composed of two perpendicular revolute joints. One of the (rR) joint axes can be reconfigured continuously, which allows the mechanism to exhibit three distinct configurations. Initially, the constraint equations are derived by using algebraic geometry approach, and the primary decomposition is computed for the three configurations. It reveals that the 3-(rR)PS metamorphic parallel mechanism can exhibit one up to two operation modes among three configurations. When the second axes of the three (rR) joints intersect at a finite point and not coplanar, the 3-(rR)PS metamorphic parallel mechanism has only one operation mode. If the second axes of the three (rR) joints are coplanar, the 3-(rR)PS metamorphic parallel mechanism has two operation modes. It is shown that both operation modes have the same motion type, namely, 1T2R motion. However, to realize the same trajectories in both operation modes, the moving platform will have different orientations. Hence, the orientation workspaces of both operation modes are characterized and the axodes are used to compare the instantaneous motion of the moving platform when passing through the same trajectories. Based on these results, an identification approach is introduced to identify which operation mode a given mechanism pose belongs to and this provides a useful method for trajectory planning.

Stiffness analysis of a metamorphic parallel mechanism with three configurations

Compared with series mechanisms, a parallel mechanism has the merits of high stiffness, fast response, and centralised layout of electric cylinders, which is more suitable for the mechanical leg of a rescue robot. However, it is not flexible enough to improve the environment adaptability of the robot. Adding the abilities of reconfiguration and mobility change to general parallel mechanisms, a novel metamorphic parallel mechanism for robotic legs is proposed based on an innovative rotatable-axis revolute joint. The inverse kinematic model of the new mechanism is established and the constraint conditions and ranges of the key parameters are explored, as well as obtaining the cloud picture of its workspace. The stiffness model is formulated with the consideration of the deformation of the main components caused by the actuation and constraints, utilising the screw theory. The stiffness matrices of the home positions of configurations I and III are then acquired and the stiffness distributions in the sub-workspace around the desired trajectory are evaluated, which are expected to lay a good theoretical foundation for the application of this novel mechanism.

A holographic matrix representation of the metamorphic parallel mechanisms

Abstract. Metamorphic mechanisms belong to the class of mechanisms that are able to change their configurations sequentially to meet different requirements. In this paper, a holographic matrix representation for describing the topological structure of metamorphic mechanisms was proposed. The matrix includes the adjacency matrix, incidence matrix, links attribute and kinematic pairs attribute. Then, the expanded holographic matrix is introduced, which includes driving link, frame link and the identifier of the configurations. Furthermore, a matrix representation of an original metamorphic mechanism is proposed, which has the ability to evolve into various sub-configurations. And evolutionary relationships between mechanisms in sub-configurations and the original metamorphic mechanism are determined distinctly. Examples are provided to demonstrate the validation of the method.

Unified inverse dynamics for a novel class of metamorphic parallel mechanisms

• A novel class of metamorphic parallel mechanism based on 3-PUPS mechanism is proposed. • The metamorphic parallel mechanism can be adapted into 32 new configurations by varying motor locking cell combinations. • A unified inverse dynamics model based on virtual working principle are established. • The derived unified inverse dynamics model has two different forms of expression, matrix form and Lagrange form. An inverse dynamics model for a novel metamorphic parallel mechanism was developed in this paper. First, the velocity relation between each moving member and the moving platform was analyzed systematically by examining the kinematics of the mechanism based on the metamorphic principle. The metamorphic parallel mechanism can be adapted into 32 configurations by various motor locking cell combinations. Second, a unified inverse dynamics model based on the virtual work principle was established. Finally, a novel 3-PUPS type metamorphic parallel mechanism was analyzed to demonstrate its universality and the correctness of the developed model.

Reconfiguration-aimed and manifold-operation based type synthesis of metamorphic parallel mechanisms with motion between 1R2T and 2R1T

This paper presents a novel approach for synthesizing metamorphic parallel mechanisms with an ability of reconfiguring motion between 1R2T and 2R1T based on quotient operation of manifolds. With the theoretical fundamentals of Lie subgroups and submanifolds, the principle of configuration change is proposed in the synthesis with a submanifold switch, that reconfigures the mechanism to provide a various motion, leading to reconfiguration of the metamorphic parallel mechanism platform. The synthesis starts from a quotient operation of manifolds to generate a manifold subchain, the synthesis of these subchains is aiming at the reconfiguration of the platform between 1R2T and 2R1T based on the same composition form of submanifold subchains with various motions. Three new subchains are synthesized with metamorphic joints, revolute joints and prismatic joints based on manifold-operation, which leads to a configuration switch of each subchain in terms of the phase change of the metamorphic joint with respect to relative positions of rotational axis and links, resulting in different constraints and motions of the subchains, leading to a platform with an ability to realize multiple motions. The design of new metamorphic joints is a key factor to realize the different motion of platform in terms of the principle of configuration change and manifold-operation. Further, the special geometrical properties and several specific phases of the metamorphic joint are analyzed. The approach of synthesis based on manifold-operation provides a distinct rationale for this paper. Under this guidance, analysis of motion and constraint conditions transmitted to the platform through subchains is essential, to enable the reconfiguration aimed type synthesis of metamorphic parallel mechanisms.

Design and Kinematic Analysis of a 3RRlS Metamorphic Parallel Mechanism for Large-Scale Reconfigurable Space Multifingered Hand

Capturing noncooperative targets in space has great prospects for aerospace application. In this work, the knuckle unit of a large-scale reconfigurable space multifingered hand (LSRSMFH) for multitask requirements is studied. A plurality of knuckle units is connected in series to form a finger of the LSRSMFH. First, the lockable spherical (lS) joint, a new metamorphic joint that can function as a Hooke (lS1) or spherical (lS2) joint and is driven by shape memory alloy (SMA) material, is proposed. Based on the lS joint, this paper presents a new metamorphic parallel mechanism (MPM) (i.e., 3RRlS MPM), which has four configurations, namely, 3RRlS1, 3RRlS2, 2RRlS1-RRlS2, and 2RRlS2-RRlS1 configuration. The degree-of-freedom (DOF), overconstraint, and parasitic motion of the 3RRlS MPM are analyzed using screw theory, of which the DOF can be changed from 1 to 3. The 3RRlS1 configuration has a virtual constraint, and the 3RRlS2 configuration has parasitic motions. The results indicate that the mechanism motion screws can qualitatively represent the mechanism parasitic motions, and it is verified by deriving the kinematic equation of the 3RRlS MPM based on its spatial geometric conditions, the workspace of the 3RRlS MPM is further solved. The kinematic analysis indicates that the 3RRlS MPM can realize the folding, capturing, and reconfiguring conditions of the LSRSMFH.

Type Synthesis of Metamorphic Parallel Mechanism with Spherical Five Bar Linkage

Type Synthesis of Metamorphic Parallel Mechanism with Spherical Five Bar Linkage

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

This paper presents a metamorphic parallel mechanism (MPM) which can switch its motion between pure translation (3T) and pure rotation (3R). This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable, and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraints of the parallel mechanism covering both 3T and 3R motion. Following this, screw theory based motion/force transmission equations are obtained, and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the MPM. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

Mobility variation of a family of metamorphic parallel mechanisms with reconfigurable hybrid limbs

This paper presents a planar metamorphic mechanism (PMM) which has three distinct working phases and a family of metamorphic parallel mechanisms with a PMM as closed-loop subchain in each limb. The study starts from analysis of mobility variation and motion characteristics in each phase of the PMM based on screw theory. Three types of reconfigurable hybrid limbs are then constructed by integrating the PMM and serial chains capable of supplying one constraint force and one constraint couple. This leads to the design of a new family of metamorphic parallel mechanisms in which the platform is connected to the base by three reconfigurable hybrid limbs. The configuration changes of the reconfigurable limb associate with the three distinct phases of the PMM are analyzed and the constraints exerted by the reconfigurable limb in various configurations are identified. The analyses reveal that the metamorphic parallel mechanisms have ability to alter the performance of platform from full 6-DOF configuration to 5-, 4- and 3-DOF configurations resorting to the internal configuration variation of the three reconfigurable limbs. Finally, actuation models with selected joints for mounting drives for the metamorphic parallel mechanisms are addressed and application cases including the potential for hybrid additive and subtractive manufacturing machine of the proposed mechanisms are discussed in details. A planar metamorphic mechanism with three working phases is proposed.Three types of hybrid reconfigurable limbs are constructed.A family of metamorphic parallel mechanisms is obtained.The metamorphic parallel mechanisms have ability to alter the performance of platform from full 6-DOF to 3-DOF.Six motors near to the base are efficient for each mechanism.

Unified kinematics and optimal design of a 3rRPS metamorphic parallel mechanism with a reconfigurable revolute joint

This paper introduces a new metamorphic parallel mechanism based on a reconfigurable revolute (rR) joint and the mechanism consists of three rRPS (rR joint-prismatic joint-spherical joint) limbs. Reconfiguration principle of the rR joint and the rRPS limb is explained, based on which the 3rRPS metamorphic parallel mechanism can be reconfigurable between two working motion types, pure rotation (3R) motion and one translation and two rotation (1T2R) motion. Using the limb geometric constraint model, analytical forward kinematics is solved in a unified way for both motion types. Reciprocal screw based Jacobian is obtained for singularity analysis which is then used for singularity-free workspace analysis. Based on those, maximum singularity-free workspace and kinematics performance based criteria are applied in optimizing basic mechanism parameters considering input and passive joint limitations. A unified objective function with variable design priorities represented by function weights of the two topologies is proposed and examples are illustrated. The introduced new parallel mechanism covers the two very useful motion types, 3R and 1T2R, while the model in the paper provides basis of modeling and optimal design for further applications.

Joint force decomposition and variation in unified inverse dynamics analysis of a metamorphic parallel mechanism

This paper presents a unified inverse kinematics and dynamics model of a metamorphic parallel mechanism with pure rotation and pure translation phases. By altering one rotation axis of the reconfigurable Hooke (rT) joints in the limbs, the mechanism can be switched into one of the two phases. To provide joint reaction forces for optimal design and control, Newton method is used in developing the dynamics model which is unified by combining geometric constraints and parameters in both phases. An analytical investigation provides special joint force decomposition and limb coordinate setup to decouple the dynamics equations between the platform and the limbs. This reduces the dynamics computation load from solving a 15 × 15 matrix to a 6 × 6 matrix. A numerical example is given to illustrate the proposed method and simulation results are explained and compared between the two phases. The work on this paper gives good reference for optimal design and control of this metamorphic parallel mechanism in different applications using two phases.

Screw-System-Variation Enabled Reconfiguration of the Bennett Plano-Spherical Hybrid Linkage and Its Evolved Parallel Mechanism

This paper presents the Bennett plano-spherical hybrid linkage and proposes a novel metamorphic parallel mechanism consisting of this plano-spherical linkage as part of limbs. In light of geometrical modeling of the Bennett plano-spherical linkage, and with the investigation of the motion-screw system, the paper reveals for the first time the reconfigurability property of this plano-spherical linkage and identifies the design parameters that lead to change of constraint equations, and subsequently to variation of the order of the motion-screw system. Arranging this linkage as part of limbs, the paper further investigates the reconfiguration property of the plano-spherical linkage evolved parallel mechanism. The analysis reveals that the platform constraint-screw system varies following both bifurcation and trifurcation with motion branch variation in the 6R linkage integrated limb structure. Consequently, this variation of the platform constraint-screw system leads to reconfiguration of the proposed metamorphic parallel mechanism. The paper presents a way of analyzing reconfigurability of kinematic structures based on the screw-system approach.

Unified Singularity Modeling and Reconfiguration of 3rTPS Metamorphic Parallel Mechanisms with Parallel Constraint Screws

This paper presents a unified singularity modeling and reconfiguration analysis of variable topologies of a class of metamorphic parallel mechanisms with parallel constraint screws. The new parallel mechanisms consist of three reconfigurable rT PS limbs that have two working phases stemming from the reconfigurable Hooke (rT) joint. While one phase has full mobility, the other supplies a constraint force to the platform. Based on these, the platform constraint screw systems show that the new metamorphic parallel mechanisms have four topologies by altering the limb phases with mobility change among 1R2T (one rotation with two translations), 2R2T, and 3R2T and mobility 6. Geometric conditions of the mechanism design are investigated with some special topologies illustrated considering the limb arrangement. Following this and the actuation scheme analysis, a unified Jacobian matrix is formed using screw theory to include the change between geometric constraints and actuation constraints in the topology reconfiguration. Various singular configurations are identified by analyzing screw dependency in the Jacobian matrix. The work in this paper provides basis for singularity-free workspace analysis and optimal design of the class of metamorphic parallel mechanisms with parallel constraint screws which shows simple geometric constraints with potential simple kinematics and dynamics properties.

Constraint-plane-based synthesis and topology variation of a class of metamorphic parallel mechanisms

This paper investigates various topologies and mobility of a class of metamorphic parallel mechanisms synthesized with reconfigurable rTPS limbs. Based on the reconfigurable Hooke (rT) joint, the rTPS limb has two phases which result in parallel mechanisms having ability of mobility change. While in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane which is used to demonstrate different topologies of the nrTPS metamorphic parallel mechanisms by investigating various relations (parallel or intersecting) among the n constraint planes (n = 2,3,..,6). Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals mobility and redundant geometric conditions of the mechanism topologies. By altering the limbs into the non-constraint phase without constraint plane, new mechanism phases are deduced with mobility change based on each mechanism topology.

Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion

This paper introduces a new metamorphic parallel mechanism consisting of four reconfigurable rTPS limbs. Based on the reconfigurability of the reconfigurable Hooke (rT) joint, the rTPS limb has two phases while in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane. This results in the mechanism to have ability of reconfiguration between different topologies with variable mobility. Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals the bifurcated motion property in the topology with mobility 2 and the geometric condition with mobility change in altering to other mechanism topologies. Following this, a unified kinematics limb modeling is proposed considering the difference between the two phases of the reconfigurable rTPS limb. This is further applied for the mechanism modeling and both the inverse and forward kinematics is analytically solved by combining phases of the four limbs covering all the mechanism topologies. Based on these, a unified singularity modeling is proposed by defining the geometric constraint forces and actuation forces in the Jacobian matrix with their change in the variable topologies in terms of constraint screws. Analysis of workspace with singularity distribution is carried out using this model and corresponding singularity loci are obtained with special singular configurations illustrated.

Reconfigurability and unified kinematics modeling of a 3rTPS metamorphic parallel mechanism with perpendicular constraint screws

This paper investigates reconfigurability and unified analytical kinematics analysis of a new 3rTPS metamorphic parallel mechanism consisting of three reconfigurable rTPS limbs in perpendicular base planes. Constraint screw systems show that in one phase the rTPS limb has no constraint to the platform and in the other phase obtained by altering the reconfigurable Hooke joint, it provides a constraint force. The two phases of the limb qualify the 3rTPS metamorphic parallel mechanism to have four topologies with ability of mobility change among 3R (three rotations), 3R1T (three rotations one translation), 3R2T and mobility 6. By considering the difference of the two phases of the limb, a unified kinematics modeling is proposed based on the actuation scheme analysis by taking one phase as a special case of the other. Following this, a unified kinematics modeling of the 3rTPS metamorphic parallel mechanism is obtained by covering all its four topologies. Both inverse and forward kinematics analysis are solved analytically and numerical examples confirm these theoretical results.