A Finite and Instantaneous Screw Based Approach for Topology Design and Kinematic Analysis of 5-Axis Parallel Kinematic Machines

Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non?redundant screws in quasi?vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two?translational and three?rotational(2T3R)5?axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthe?sized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.

THE EXISTENCE AND UNIQUENESS OF THE SCREW TENSOR FOR THE FINITE DISPLACEMENT OF A RIGIDBODY

The existence and uniqueness theorem of the screw tensor for the finite displacement of a rigidbody is proposed and then proved using the screw calculus. As a conseguence, formulae are obtained for determining the screw tensor in terms of the finite displacement data of the rigidbody.

Task-Oriented Topology System Synthesis of Reconfigurable Legged Mobile Lander Integrating Active and Passive Metamorphoses

To explore hostile extraterrestrial landforms and construct an engineering prototype,this paper presents the task-oriented topology system synthesis of reconfigurable legged mobile lander(ReLML)with three operation modes from adjusting,landing,to roving.Compared with our preceding works,the adjusting mode with three rotations(3R)provides a totally novel exploration approach to geometrically matching and securely arriving at complex terrains dangerous to visit currently;the landing mode is redefined by two rotations one translation(2R1T),identical with the tried-and-tested Apollo and Chang'E landers to enhance survivability via reasonable touchdown buffering motion;roving mode also utilizes 2R1T motion for good motion and force properties.The reconfigurable mechanism theory is first brought into synthesizing legged mobile lander integrating active and passive metamorphoses,composed of two types of metamorphic joints and metamorphic execution and transmission mechanisms.To reveal metamorphic principles with multiple finite motions,the finite screw theory is developed to present the procedure from unified mathematical representation,modes and source phase derivations,metamorphic joint and limb design,to final structure assembly.To identify the prototype topology,the 3D optimal selection matrix method is proposed considering three operation modes,five evaluation criteria,and two topological subsystems.Finally,simulation verifies the whole task implementation process to ensure the reasonability of design.

A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism

Topology and performance are the two main topics dealt in the development of robotic mechanisms.However,it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame.As the properties associated with topology and performance,finite motion and instantaneous motion of the robot play key roles in the procedure.On the purpose of providing a fundamental preparation for integrated modeling and design,this paper carries out a review on the existing unified mathematic frameworks for motion description and computation,involving matrix Lie group and Lie algebra,dual quaternion and pure dual quaternion,finite screw and instantaneous screw.Besides the application in robotics,the review of the work from these mathematicians concentrates on the description,composition and intersection operations of the finite and instantaneous motions,especially on the exponential-differential maps which connect the two sides.Furthermore,an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development.The presented review offers insightful investigation to the motion description and computation,and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.

Space truss construction modeling based on on-orbit assembly motion feature

More space truss construction has been planned to develop and utilize space resources.These trusses are designed in the way of large-scale,complex,modular,and on-orbit assembly.To meet the upcoming challenge of large-scale space infrastructure construction,it is necessary to study space truss automation design and robotic construction.This paper proposes an ordinal finite screw adjacency matrix model(OFSAMM),focusing on the relationship between assembly motions,to express and compute a space truss structure.In this model,a space truss is abstracted as a set of ordered assembly motions,each of which is recorded as a finite screw as the basic element of the truss and its assembly.The operation of truss transformation is also derived under this model.Therefore,the truss configuration,the assembly sequence,the truss sub-assembly,the truss components,and the on-orbit assembly task can be expressed and calculated in a unified model,which is calculated and stores the truss topology and assembly with the minimum storage cost.At the end of this paper,we introduce how to synthesize and optimize space truss design through two cases.The study will help to improve design efficiency.Furthermore,it provides a theoretical basis for the automatic construction of space truss structures,especially in the next stage.