METAMORPHIC MECHANISMSAND THEIR CONFIGURATION MODELS

The concept of metamorphic mechanisms is presented, configuration models and configuration transformations relating to a set of new matrix operations are discussed and proposed. The configuration of a metamorphic mechanism reflects the connectivity change in the mechanism during motions which results in mobility change and presents the characteristics of the mechanism which is discussed in various applications particularly in decorative artifacts. The characteristics is further investigated with mobility analysis.

Structural Synthesis of Compliant Metamorphic Mechanisms Based on Adjacency Matrix Operations

A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s＋1 links from an s-link mechanism （the final configuration）. The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.

Configuration Analysis of Metamorphic Mechanisms Based on Extended Adjacency Matrix Operations

The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can easily be simulated by computer.But the adjacency matrix based on monochrome topological graph is not suitable for the topological representation of mechanisms with multiple joints.The method of adjacency matrix operations has its own limitations for analysis of configuration transformation of metamorphic mechanisms because it can only be used in the topological representation of mechanisms with single joints.In order to overcome the drawback of the adjacency matrix,a kind of new matrix named as extended adjacency matrix is proposed to express topological structures of all mechanisms.The extended adjacency matrix is not only suitable for the topological representation of mechanisms with single joints,but also can be used in that of mechanisms with multiple joints.On this basis,a method of matrix operations based on the extended adjacency matrix is proposed to analyze the configuration transformation of metamorphic mechanisms.The method is not only suitable for configuration analysis of metamorphic mechanisms with single joints as well as metamorphic mechanisms with multiple joints.The method is evaluated by calculating two examples representing metamorphic mechanisms with single joint and multiple joints respectively.It can be concluded that the method is effective and correct for analysis of configuration transformation of all metamorphic mechanisms.The proposed method is simple and easy to be achieved by computer programming.It provides a basis for structural synthesis of all metamorphic mechanisms.

An optimization method for metamorphic mechanisms based on multidisciplinary design optimization

The optimization of metamorphic mechanisms is different from that of the conventional mechanisms for its characteristics of multi-configuration. There exist complex coupled design variables and constraints in its multiple different configuration optimization models. To achieve the compatible optimized results of these coupled design variables, an optimization method for metamorphic mechanisms is developed in the paper based on the principle of multidisciplinary design optimization（MDO）. Firstly, the optimization characteristics of the metamorphic mechanism are summarized distinctly by proposing the classification of design variables and constraints as well as coupling interactions among its different configuration optimization models. Further, collaborative optimization technique which is used in MDO is adopted for achieving the overall optimization performance. The whole optimization process is then proposed by constructing a two-level hierarchical scheme with global optimizer and configuration optimizer loops. The method is demonstrated by optimizing a planar five-bar metamorphic mechanism which has two configurations,and results show that it can achieve coordinated optimization results for the same parameters in different configuration optimization models.

DYNAMIC MODELING OF METAMORPHIC MECHANISM

The concept of metamorphic mechanism is put forward according to the changeof configurations from one state to another. Different configurations of metamorphic mechanism aredescribed through the method of Huston lower body arrays. Kinematics analyses for metamorphicmechanism with generalized topological structure, including the velocity, angular velocity,acceleration and angular acceleration, are given. Dynamic equations for an arbitrary configuration,including close-loop constraints, are formed by using Kane's equations. For an arbitrary metamorphicmechanism, the transformation matrix of generalized speeds between configuration zeta and zeta+1 isobtained for the first time. Furthermore, configuration-complete dynamic modeling of metamorphicmechanism including all configurations is completely established.

A Biomimetic Study of Discontinuous-Constraint Metamorphic Mechanism for Gecko-Like Robot

Locomotion ability, efficiency and reliability are key targets for a good robot. The linkage mechanism for robot locomotion is a discontinuous-constraint metamorphic mechanism. Here we set up equations to present the discontinuous-constraint, point out that driving and controlling are the key points to improve the performance and efficiency of the linkage mechanism. Inspired by controlling strategy of the motor nervous system in peripheral vertebrae to the locomotion, we draw off motor control and drive strategy.

Practical Structural Design Approach of Multiconfiguration Planar Single‑Loop Metamorphic Mechanism with a Single Actuator

As a type of multiconfiguration mechanism that can operate in an under-actuated state,metamorphic mechanisms were proposed more than two decades ago and attracted significant interest.Studies on structural synthesis of metamorphic mechanisms tend to focus more on metamorphic techniques and the structural synthesis of source mechanisms for metamorphic mechanisms.By designing different constraint architectures of metamorphic joints,multistructures can be obtained from the same source metamorphic mechanism.To determine the constraint architectures of metamorphic joints and their different assembly combinations,a kinematic status matrix and a corresponding constraint status matrix are constructed based on the metamorphic cyclogram of a source mechanism.According to the equivalent resistance gradient model and the constraint status matrix,an equivalent resistance matrix for the metamorphic joints is proposed.A structural synthesis matrix of the metamorphic mechanism is then obtained from the equivalent resistance matrix by deducing the constraint form vectors of the metamorphic joints.Furthermore,a kinematic diagram synthesis of the source metamorphic mechanism of a planar single-loop metamorphic mechanism is proposed,which is based on only the 14 one-or zero-degrees-of-freedom linkage groups.The entire structural design method of a metamorphic mechanism is based on the structural synthesis matrix and is presented as a systematic process.Finally,the proposed structural design approach is illustrated by two examples to verify its feasibility and practicality.This study provides an effective method for designing a practical multi-mobility and multiconfiguration planar single-loop metamorphic mechanism with a single actuator.

Metamorphic Manipulating Mechanism Design for MCCB Using Index Reduced Iteration

The present research on moulded case circuit breaker（MCCB） focuses on the enhancement of current-limiting interrupting performance during short circuit, overload, under voltage and phase failure, involving electrics, magnetic, mechanics, thermal, material, friction, arc extinguishing, impact vibration, skin effect, etc. The rigid-flexible coupling of the parts and components of the metamorphic manipulating mechanism in multi-fields leads to the non-rigid, high frequency, high damping, singularity of the Euler-Lagrange equations which represents the multi-body dynamics. The small step iteration which is used for obtaining the instantaneous and short time critical interrupting performance of metamorphic mechanism appears inaccuracy. It is difficult to realize top-down design by existing CAD systems. Therefore, a metamorphic manipulating mechanism design method for MCCB using index reduced iteration（IRI） is put forward. The metamorphic manipulating mechanism of MCCB is decomposed into three mechanisms： main switch connector mechanism, electromagnet-drawbar-jump buckle mechanism, and bimetallic strip-drawbar mechanism, which is respectively described by electro-dynamic force, electromagnet force, and bimetallic strip force. The dummy part（virtual rigid） without moment of inertia and mass is employed as intermediate to join the flexible body and rigid body. The model of rigid-flexible coupling metamorphic mechanism multi-body dynamics is built. The differential algebraic equations（DAEs） of the multibody dynamics model are converted to pure ordinary differential equations（ODEs） by coordinate partition. Order reduced integration with multi-step and variable step-size is preceded based on IRI. The non-linear algebraic equations are solved in each integration step by Newton-Rapson iteration. There is no ill-condition and singularity of Jacobian matrix when step size reduces to zero. The independent prototype design system using ACIS R13, HOOPS V11.0 and Visual C＋＋.NET 2003 has been developed, which verifies the effectiveness of the proposed method. The proposed method enhances the current-limiting interrupting performance of MCCB, and has reference significance for multi-body dynamics design for similar flexible metamorphic mechanisms in multi-fields.

Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms

The current research of reconfigurable parallel mechanism mainly focuses on the construction of reconfigurable joints.Compared with the method of changing the mobility by physical locking joints,the geometric constraint has good controllability,and the constructed parallel mechanism has more configurations and wider application range.This paper presents a reconfigurable axis(rA)joint inspired and evolved from Rubik’s Cubes,which have a unique feature of geometric and physical constraint of axes of joint.The effectiveness of the rA joint in the construction of the limb is analyzed,resulting in a change in mobility and topology of the parallel mechanism.The rA joint makes the angle among the three axes inside the groove changed arbitrarily.This change in mobility is completed by the case illustrated by a 3(rA)P(rA)reconfigurable parallel mechanism having variable mobility from 1 to 6 and having various special configurations including pure translations,pure rotations.The underlying principle of the metamorphosis of this rA joint is shown by investigating the dependence of the corresponding screw system comprising of line vectors,leading to evolution of the rA joint from two types of spherical joints to three types of variable Hooke joints and one revolute joint.The reconfigurable parallel mechanism alters its topology by rotating or locking the axis of rA joint to turn all limbs into different phases.The prototype of reconfigurable parallel mechanism is manufactured and all configurations are enumerated to verify the validity of the theoretical method by physical experiments.

Constraint Force Analysis of Metamorphic Joints Based on the Augmented Assur Groups

In order to obtain a simple way for the force analysis of metamorphic mechanisms, the systematic method to unify the force analysis approach of metamorphic mechanisms as that of conventional planar mechanisms is proposed. A force analysis method of metamorphic mechanisms is developed by transforming the augmented Assur groups into Assur groups, so that the force analysis problem of metamorphic mechanisms is converted into the force analysis problems of conventional planar mechanisms. The constraint force change rules and values of metamorphic joints are obtained by the proposed method, and the constraint force analysis equations of revolute metamorphic joints in augmented Assur group RRRR and prismatic metamorphic joints in augmented Assur group RRPR are deduced. The constraint force analysis is illustrated by the constrained spring force design of paper folding metamorphic mechanism, and its metamorphic working process is controlled by the spring force and geometric constraints of metamorphic joints. The results of spring force show that developped design method and approach are feasible and practical. By transforming augmented Assur groups into Assur groups, a new method for the constraint force analysis of metamorphic joints is proposed firstly to provide the basis for dynamic analysis of metamorphic mechanism.

Anatexis,Deformation and Exhumation Mechanism for UHP Metamorphic Rocks:A Case Study in the North Qaidam and South Altyn UHP Terrane,Western China

Objective In recent years,hydrous silicate melts by dehydrationdriven in situ partial melting constrained from experiments and natural rocks have been increasingly recognized in UHP rocks,indicating partial melting of UHP slab.Partial melting of UHP metamorphic rocks can dramatically affect the rheology of deeply subducted crust and thus play a crucial role in accelerating the exhumation of UHP slabs.

A Method for the Configuration Design of a Space Truss Deployable Mechanism and Its Application

A method based on the metamorphic principle is proposed for the analysis of the configuration design of a space truss deployable mechanism. The configuration change and correspondent topological graphs and adjacency matrixes at different work-stage of the mechanism, which is helpful to completely understand the composition and change rules of the metamorphic mechanism, are analyzed to indicate the metamorphic relationship in one working cycle. Furthermore, the static distance matrix, dynamic distance matrix and stiffness matrix of the mechanism are derived to assess the ability of the designed configuration to reveal some of the topological characteristics like compactness, dynamic sensitivity and stiffness. Using this proposed method in a space truss deployable mechanism helps the designer to evaluate its performance at the conceptual stage of design and make a rapid, reasonable selection for configuration design, which provides means for processing its type of analysis by computer.