Joint workspace of parallel kinematic machines

Robot workspace is the set of positions a robot can reach. Workspace is one of the most useful measures for the evaluation of a robot. Workspace is usually defined as the reachable space of the end-effector in Cartesian coordinate system. However, it can be defined in joint coordinate system in terms of joint motions. In this paper, workspace of the end-effector is called task workspace, and workspace of the joint motions is called joint workspace. Joint workspace of a parallel kinematic machine (PKM) is focused, and a tripod machine tool with three degrees of freedom (DOF) is taken as an example. To study the joint workspace of this tripod machine tool, the forward kinematic model is established, and an interpolating approach is proposed to solve this model. The forward kinematic model is used to determine the joint workspace, which occupies a portion of the domain of joint motions. The following contributions have been made in this paper include: (i) a new concept so-called joint workspace has been proposed for design optimization and control of a PKM; (ii) an approach is developed to determine joint workspace based on the structural constraints of a PKM; (iii) it is observed that the trajectory planning in the joint coordinate system is not reliable without taking into considerations of cavities or holes in the joint workspace.     

Kinematic modeling of Exechon parallel kinematic machine

The studies on PKMs have attracted a great attention to robotics community. By deploying a parallel kinematic structure, a parallel kinematic machine (PKM) is expected to possess the advantages of heavier working load, higher speed, and higher precision. Hundreds of new PKMs have been proposed. However, due to the considerable gaps between the desired and actual performances, the majorities of the developed PKMs were the prototypes in research laboratories and only a few of them have been practically applied for various applications; among the successful PKMs, the Exechon machine tool is recently developed. The Exechon adopts unique over-constrained structure, and it has been improved based on the success of the Tricept parallel kinematic machine. Note that the quantifiable theoretical studies have yet been conducted to validate its superior performances, and its kinematic model is not publically available. In this paper, the kinematic characteristics of this new machine tool is investigated, the concise models of forward and inverse kinematics have been developed. These models can be used to evaluate the performances of an existing Exechon machine tool and to optimize new structures of an Exechon machine to accomplish some specific tasks.     

Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy

High precision is still one of the challenges when parallel kinematic machines are applied to advanced equipment. In this paper, a novel planar 2-DOF parallel kinematic machine with kinematic redundancy is proposed and a method for redundant force optimization is presented to improve the precision of the machine. The inverse kinematics is derived, and the dynamic model is modeled with the Newton–Euler method. The deformations of the kinematic chains are calculated and their relationship with kinematic error of the machine is established. Then the size and direction of the redundant force acting on the platform are optimized to minimize the position error of the machine. The dynamic performance of the kinematically redundant machine is simulated and compared with its two corresponding counterparts, one is redundantly actuated and the other is non-redundant. The proposed kinematically redundant machine possesses the highest position precision during the motion process and is applied to develop a precision planar mobile platform as an application example. The method is general and suitable for the dynamic modeling and redundant force optimization of other redundant parallel kinematic machines.     

Comparative analysis of a new 3×PPRS parallel kinematic mechanism

Parallel Kinematic Mechanisms (PKMs) are well suited for high-accuracy applications. However, constraints such as end-effector rotation (i.e., platform tilt angle) and configuration-dependent stiffness often limit their usage. A new six degree-of-freedom (dof) PKM architecture based on a 3×PPRS topology that addresses these concerns is presented in this paper – specifically, the proposed PKM can achieve high (end-effector) tilt angles with enhanced stiffness. The mechanism is also compared with similar three known 6-dof architectures, through which it is shown that the proposed PKM indeed exhibits higher stiffness relative to these three reference PKMs. The static stiffness is derived using matrix structural analysis, and the dynamic stiffness is obtained via finite-element analysis. A prototype of the proposed PKM that was designed and built is presented.     

Analysis of parallel kinematic machine with kinetostatic modelling method

A new method, called Kinetostatic Modelling Method is proposed for analysis of parallel kinematic machines (PKMs) in the paper. First, system modelling includes mobility study, kinematic model and inverse kinematic is conducted. Then, kinetostatic modelling is presented. It includes a complete compliant model developed for the analysis of the PKMs with fixed-length legs, with the model, two global compliance indices are introduced to provide a new mean of measuring the PKM's compliance over the workspace. These two global indices are the mean value and the standard deviation of the trace of the generalized compliance matrix. The mean value represents the average compliance of the PKM over the workspace, while the standard deviation indicates the compliance fluctuation relative to the mean value. The effect of three types of compliance is investigated in order to identify a dominant factor. The proposed method is implemented to analyze the compliance of the Tripod-based PKM prototype built at the Integrated Manufacturing Technologies Institute of the National Research Council of Canada. It is shown that the proposed method is an effective means for evaluating the kinetostatic behaviour of PKMs globally.     

The kinematic analyses of the 3-DOF parallel machine tools

A 3-degree-of-freedom (3-DOF) parallel machine tool based on a tripod mechanism is developed and studied. The kinematics analysis is performed, the workspace is derived, and an analysis on the number of conditions of the Jacobian matrix and manipulability is carried out. A method for error analysis and manipulability is introduced. Hence, the manipulability analysis of the parallel machine tool is accomplished.     

Vision-based self-calibration and control of parallel kinematic mechanisms without proprioceptive sensing

This work is a synthesis of our experience over parallel kinematic machine control, which aims at changing the standard conceptual approach to this problem. Indeed, since the task space, the state space and the measurement space can coincide in this class of mechanisms, we came to redefine the complete modelling, identification and control methodology. Thus, it is shown in this paper that, generically and with the help of sensor-based control, this methodology does not require any joint measurement, thus opening a path to simplified mechanical design and reducing the number of kinematic parameters to identify. This novel approach is illustrated on the reference parallel kinematic mechanism (the Gough–Stewart platform) with vision as the exteroceptive sensor. This work was supported by European Community through the Integrated Project NEXT number 0011815. It was initially published in the Proceedings of the 13th International Conference on Advanced Robotics (ICAR’07), Jeju, Korea, 21–24 August 2007 [3]. During this work, Philippe Martinet was holding a visiting professor position at the Intelligent Service Robotics Center at Sungkyunkwan University, Suwon, South Korea.     

Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling

This paper deals with the performance analysis of a 3-degree-of-freedom (3-DOF) planar parallel manipulator with actuation redundancy. Closed-form solutions are developed for both the inverse and direct kinematics about the redundant parallel manipulator. In performance analysis phase, the dexterity is analyzed, three kinds of singularities are investigated, and the stiffness is estimated. Compared with the corresponding non-redundant parallel manipulator with the redundant link removed, the redundantly actuated one has better dexterity, litter singular configurations and higher stiffness. The redundantly actuated parallel manipulator was applied to the design of a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.     

On nonassembly in the optimal dimensional synthesis of planar mechanisms

This paper presents a general method for treating nonassembly in the optimal synthesis of planar mechanisms. The synthesis is performed with gradient based optimization algorithms and the sensitivities are calculated analytically through the method of direct differentiation. The analysis is based on the well-established and general method of computational kinematics. In this study the residuals of the joint constraint equations are minimized rather than equated to zero. This makes it possible to perform the kinematic analysis for any proposed design even though it may not be possible to assemble the mechanism. Several examples are provided. Received July 25, 2000     

Accuracy synthesis of a multi-level hybrid positioning mechanism for the feed support system in FAST

This study examines the terminal accuracy synthesis of a multi-level hybrid positioning mechanism for the feed support system in a Five-hundred-meter Aperture Spherical Radio Telescope (FAST) project, specifically considering three types of error influence factors such as time-varying barycenter, geometric error, and structural deformation. An error model caused by a time-varying barycenter and that for the entire mechanism are first established, and the physical meaning of the latter is further explained. The three factors that influence terminal accuracy are then analyzed. An efficient approach for acquiring the terminal error boundary over the entire workspace is proposed on the basis of the vector set theory and a linear algebra method. After employing an error compensation method for the first-level mechanism through control strategy, terminal accuracy synthesis is conducted by using a nonlinear optimization algorithm. Both constraints for accuracy and weight are satisfied after introducing measurement systems. Moreover, the proposed method of accuracy analysis and synthesis can be applied to other multi-level hybrid mechanisms.     

Type synthesis of a class of spatial lower-mobility parallel mechanisms with orthogonal arrangement based on Lie group enumeration

Type synthesis of lower-mobility parallel mechanisms (PMs) has drawn extensive interests, particularly two main approaches were established by using the reciprocal screw system theory and Lie group theory, respectively. Although every above approach provides a universal framework for structural design of general lower-mobility PMs, type synthesis is still a comparably difficult task for the PMs with particular geometry or required to fulfill some specified tasks. This paper aims at exploring a simple and ef...     

Type synthesis of the rotational decoupled parallel mechanism based on screw theory

With the gradual deepening of study on the parallel mechanism,the difficulty brought by the existence of coupling to the theoretical analysis and practical application of parallel mechanisms is becoming increasingly apparent.The research on the decoupled parallel mechanism is currently one of the hot fields.Though most of the rotational parallel mechanisms,which has been widely used in spatial orientation fields,are not decoupled.It is comparative difficult for the synthesis of fully decoupled rotational pa...     

Type synthesis,unified kinematic analysis and prototype validation of a family of Exechon inspired parallel mechanisms for 5-axis hybrid kinematic machine tools

To fully disclose potential configurations of parallel mechanisms (PMs) that are performance-comparable to the commercially successful Exechon, a family of one translational two rotational (1T2R) over-constrained Exechon inspired PMs is synthesized through the screw theory. The synthesized PMs are further comparatively analyzed in terms of inverse kinematics, singularity occurrence and reachable workspace based on a unified kinematic model. The kinematic analyses indicate that the inherited overconstraints benefit for eliminating the constraint singularity of all synthesized Exechon inspired PMs and the workspace distribution of an Exechon inspired PM is closely related to its topological arrangement. Based on the kinematic evaluations, a preferred configuration of 2UPR-1RPS PM (‘R’: revolute joint, ‘U’: universal joint, ‘S’: spherical joint, ‘P’: prismatic actuated joint) is selected as a candidate for 1T2R spindle head. A laboratory prototype is fabricated and experimentally tested to verify the feasibility of the type synthesis and the correctness of the kinematic analyses. By integrating the selected PM with a 2-degree of freedom sliding gantry, a full scale prototype of a novel hybrid kinematic machine tool is developed to perform 5-axis machining tasks. The well match between the machined workpiece and its designed shape fully proves the engineering potential of the synthesized PMs that are expected to be employed as the functional module to construct 5-axis serial-parallel hybrid machining devices.     

A parallel processing model for the study of possible pattern recognition mechanisms in the brain

An electronic model, based on parallel processing concept and able to identify a series of patterns without requiring sophisticated technology, is presented. A receptive part transduces the pattern images into electrical signals and a processing part identifies them. The basic element of the processing part is a “pattern detecting” unit which produces a maximal response for one specific pattern presented on the receptive matrix. A set of 11 “pattern detecting” units allows the model to recognize simple patterns under various conditions and through a neural-like organization, to identify them regardless of their position or size.     

并行打印适配器在主机与非打印机外设之间实现数据传输中的应用

本文介绍了并行打印机端口在主机与非打印机外设之间进行数据传输中的应用。给出了接口电路设计的方框图，和数据输入输出的子过程，并指出了进一步的工作方向。     

6-SPS并联机床加工过程仿真

针对并联机床研究不断深入的现状，介绍了6－SPS并联机构以及加工过程仿真研究的意义，采用VC＋＋6．0OpenGL开发了6－SPS并联机床加工过程仿真系统，对各功能模块进行了简单介绍，并以单叶双曲面为例，进行了轨迹规划以及加工过程仿真，验证了仿真系统的正确性及实用性。     

并行与分布式仿真时间推进同步机制综述

并行分布仿真对复杂大规模动态系统的研究以及探索,对长远的应用提供了便利,目前已成为研究的热点。然而时间同步管理是关注并确保并行分布仿真正确执行的一种机制,它不但要确保正确的执行因果逻辑关系,而且要保证仿真系统的可重复性。时间管理是影响并行分布仿真系统高效运行的重要因素之一。在分别论述四类基本的时间推进同步机制,即保守机制、乐观机制、混合机制和自适应机制的同时,还分析了各自的优缺点,指出了今后的研究发展方向。     

A hybrid strategy for the time- and energy-efficient trajectory planning of parallel platform manipulators

In planning the trajectories of motor-driven parallel platform manipulators, the objective is to identify the trajectory which accomplishes the assigned motion with the minimal travel time and energy expenditure subject to the constraints imposed by the kinematics and dynamics of the manipulator structure. In this study, the possible trajectories of the manipulator are modeled using a parametric path representation, and the optimal trajectory is then obtained using a hybrid scheme comprising the particle swarm optimization method and the local conjugate gradient method. The numerical results confirm the feasibility of the optimized trajectories and show that the hybrid scheme is not only more computationally efficient than the standalone particle swarm optimization method, but also yields solutions of a higher quality.     

Kinematic analysis and optimal design of a novel 1T3R parallel manipulator with an articulated travelling plate

Driven by the requirements of the large-scale component assemblage for the docking platform, this paper proposes a novel one-translational-three-rotational (1T3R) parallel manipulator with an articulated travelling plate, which can provide high stiffness and good accuracy performances in the assemblage. The underlying architecture of this manipulator is briefly addressed with emphasis on the practical realization of the articulated travelling plate. On the basis of the kinematic analysis of the 1T3R parallel manipulator, its optimal design considering the force and motion transmissibility is carried out, in which the generalized virtual power transmissibility of this manipulator is defined. This paper aims at laying a solid theoretical and technical foundation for the prototype design and manufacture of the 1T3R parallel manipulator.