Configuration Evolution Method of Stewart Platform Based on Finite Screw Theory

The complete Jacobian matrix of a lower-mobility parallel mechanism is a six by six matrix that consists of the actuation sub-matrix and the constraint sub-matrix. As the alge-braic feature of the former one cannot account for the related constraint characteristics, modeling complete six by six Jaco-bian matrix becomes necessary in the kinematic analysis and optimal design of geometric parameters of this kind of parallel mechanisms. A method for deducing the complete Jacobian matrix of an incompletely symmetrical lower-mobility parallel mechanism is illustrated by taking 2RPS-2UPS as an example based on the theory of reciprocal screw. Firstly, the systems of twists and reciprocal screws of the constraint limbs are estab-lished based on the screw theory, then the constraint sub-matrix is obtained through the orthogonal product. Secondly, by lock-ing active joints of each limb, the system of additional recipro-cal screws of both constraint and unconstraint limbs is estab-lished, then the actuation sub-matrix is also obtained through the orthogonal product. By integrating these two sub-matrices properly, the complete Jacobian matrix of an incompletely symmetrical lower-mobility parallel mechanism can be finally set up. In the end, the singular conditions of 2RPS-2UPS paral-lel mechanism are analyzed by investigating the ranks of the Jacobian matrices.

The singularity-free zones of 3-RRR (R denotes actuator joint) planar parallel mechanisms are studied. The methods and procedures of determination of maximal singularity-free zone of planar 3-RRR parallel mechanism, both for centered on given point and for in the whole workspace, are introduced. For 3-RRR parallel mechanism, the expression for the singularity locus and the algorithms for determining the singularity-free zones involve both the Cartesian and the joint variables. To make the algorithms to be simplified and be efficient, the methods to simplify the algorithms for determining the singularity-free zones in Polar space is proposed. The methodology and procedures for determining the singularity-free zones centered on given point of 3-RRR planar parallel mechanisms are introduced. Then a self-modifying technique for searching the center of the whole workspace maximal singularity-free zone was developed, so that the theoretical center of the whole workspace maximal singularity-free zone can be obtained step by step automatically. The calculating results show that the simplified algorithms and the techniques for determining the singularity-free zones of planar parallel mechanism are correct and efficient.

In this paper, a novel numerical approach is proposed for workspace determination of parallel mechanisms. Compared with the classical numerical approaches, this presented approach discretizes both location and orientation of the mechanism simultaneously, not only one of the two. This technique makes the presented numerical approach applicable in determining almost all types of workspaces, while traditional numerical approaches are only applicable in determining the constant orientation workspace and orientation workspace. The presented approach and its steps to determine the inclusive orientation workspace and total orientation workspace are described in detail. A lower-mobility parallel mechanism and a six-degrees-of-freedom Stewart platform are set as examples, the workspaces of these mechanisms are estimated and visualized by the proposed numerical approach. Furthermore, the efficiency of the presented approach is discussed. The examples show that the presented approach is applicable in determining the inclusive orientation workspace and total orientation workspace of parallel mechanisms with high efficiency.

In this paper, an underactuated biomimetic octopus hand with good adaptability to the shape and size of the grasping object in unknown environment is presented. Based on the grasping task, a quadpod parallel mechanism is introduced as the basic unit of octopus hand in order to make it more flexible. Mobility of the basic unit is calculated as lower-mobility parallel mechanism (PM) by using the screw theory, this basic unit has fewer than six degrees of freedom, which was also verified by the general Grubler-Kutzbach criterion. Two different grasping methods are compared and discussed. Kinematic data of the hand have been obtained from the robotic kinematic equations and three different actuated methods are compared and discussed. The analysis in this paper shows that each unit of the underactuated mechanism has the ability of deformation and can adapt to the irregular shape of non-cooperative objects.

Parallel mechanisms with multiple links have been expected to be used in machining because they are higher in rigidity, accuracy, and output power than series mechanisms, such as industrial robots. However, unlike conventional machine tools, which consist of linear and rotary axes, parallel mechanisms have a large number of error factors. In the parallel link mechanism, there is no guide surface that physically guarantees linearity, and all accuracy is determined by the operating performance of the composite axes. This makes it difficult to identify any error factors. Therefore, a kinematics model is devised, and the behavior of the tool tip is checked by inputting the encoder information during the actual operation of a specific axis. Based on the results, we evaluate the machining characteristics of the target machine tool. The target machine tool in this study is a 5-axis machine tool that combines a 3-DOF parallel mechanism consisting of three linear motion axes and a 2-DOF serial mechanism consisting of two rotary axes. In our previous research, we tried to build a forward kinematics model. Although its prediction accuracy was insufficient, it was possible to actually identify the cause of the defect in the quality of the machined surface using the servo position information of the kinematics machine. However, we have not been able to construct an inverse kinematics model that is suitable for calculating the correction position command value to improve the quality of the machined surface. In this study, based on the shape creation theory, we devise and evaluate the kinematics model of a robotic machine tool that has a parallel mechanism. As a result of comparing the kinematics model with the 3D-CAD model in order to evaluate the accuracy of the former, it was confirmed that the proposed method has high simulation accuracy. Then, machining tests were carried out to evaluate the machining accuracy by measuring, based on proposed kinematics model, the machined surfaces in order to identify the mechanism that affects the texture of the machined surface. In addition, we performed a circle interpolation to confirm the effects of reversing the motion of each drive axis on the behavior of the tool tip. As a result, it is considered that the linear motion axis has a large effect on the behavior of the tool tip on the quadrant glitch of each drive axis. It was also found that the effects of the 1st- and 3rd-axes on the behavior of the tool tip are different from those of the 2nd-axis.

Synthesis and structure analysis of kinematic structures of 6-dof parallel robotic mechanisms

This paper presents a novel three degrees of freedom (3-DOF) planar parallel mechanism with a 360-degree rotational capability, which can be used as a positioning device. A high rotational capability is necessary to reduce process time and to apply the mechanism to various fields such as micro-machining and printed circuit board (PCB) depaneling. The proposed mechanism has the advantage of a continuous rotational capability over existing planar parallel mechanisms with limited rotation. The position and velocity kinematics are derived, and the singularities are analyzed based on the Jacobian matrices. The workspace can be determined not to have a singularity inside, and the kinematic variables for enlarging the singularity-free workspace are determined. The application example on the PCB depaneling process is proposed for future work.

A novel parallel mechanism with bifurcated motion is introduced by integrating a discontinuously movable mechanism in the limb design. The mechanism has instantaneously six degrees of freedom at a singularity point. With the discontinuously movable mechanism moving to different motion branches, the parallel mechanism has the ability to evolve into four configurations with different motion characteristics, including 3T motion configuration, 3R motion configuration, 2T1R motion configuration and 2R1T motion configuration. By rigidizing the input joints, the rationality of input scheme for this mechanism is identified based on screw theory. Six motors nearly mounted to the base can sufficiently drive the parallel mechanism to switch between different motion configurations and perform different motions. The forward and inverse kinematics of the mechanism in different configurations are given. The translational motions are independent with each other and decoupled with the rotational motions. Kinematics simulation is performed for the parallel mechanism and the results show that theoretical analyses are correct. The workspace of the parallel mechanism in a general configuration is given. Key words}Discontinuously movable mechanism Parallel mechanism Bifurcated motion Kinematics

This paper introduced a three degree-of-freedom planar parallel mechanism which is composed of three branches. In order to give directions for the following engineering design of the mechanism, the inverse kinematics and forward kinematics of this parallel mechanism are analyzed, which shows that analytical equations for the inverse and forward kinematics of the novel parallel mechanism can be obtained. Also, velocity jacobian matrix are presented, based on these matrix, solution formulas about velocity,acceleration and statics of this mechanism are derived. The analysis results show that this novel parallel mechanism can easily realize real-time control and have valuable engineering applications.

Typical parallel mechanisms suffer from parallel singularity due to kinematic coupling of multichains. This paper investigates how to remove parallel singularities by using redundant actuations. First, actuation wrenches and constraint wrenches forming the full direct kinematic Jacobian matrix are derived. After briefly addressing conditions for their constraint singularities, Grassmann–Cayley algebra is employed to identify parallel singularities. Then, employing Grassmann line geometry, the locations and the minimum number of redundant actuators are identified for the parallel mechanisms to have parallel singularity-free workspace. Three different types of 3-degree-of-freedom parallel mechanisms such as planar, spherical, and spatial parallel mechanisms are given as exemplary devices.

In this paper, parallel link mechanisms for multi drive linear motors (MDLMs) are proposed. The multi drive is a control method for linear motors in which a number of moving parts are individually driven on one stator part. Various configurations of parallel link mechanisms which were constructed for MDLMs are proposed. These mechanisms offer a wide range of motion in addition to the existing characteristics that parallel mechanisms provide, namely, rigid mechanisms, high precision, and high speed. Moreover, they are suitable for force control because of their low friction direct drive actuators. In this paper, the kinematic and dynamic characteristics of 2-DOF (xy) and 3-DOF (xy¿) planar parallel link mechanisms are investigated. A singularity analysis and internal force control method for a 3-DOF with 4 redundant moving parts is derived. The condition of dynamic decoupling and the constant inertia design of a 2-DOF with 2 moving parts and a 3-DOF with 4 moving parts are derived. The effectiveness of these analyses is then confirmed by numerical simulation. Based on this analysis, a prototype of the 3-DOF with 4 moving parts is designed and developed.

Development of a novel integrated automated assembly system for large volume components in outdoor environment

The 4TPS-PS parallel platform designed for a stabilization and automatic tracking system is a novel lower-mobility parallel mechanism. In the first part of this paper, the structure of the platform is described and the kinematics model is built. The workspace of the platform is defined as the full reachable rotation workspace when the Z coordinate dimension of the upper plate varies continuously. A fast searching method of the full reachable workspace is presented, after which the inverse kinematics of the platform is deduced. The forward and inverse solutions of the speed and force of the platform are deduced. According to the characteristic of the 4TPS-PS platform’s structure, a fast searching algorithm of the maximum generalized speed and maximum generalized force output by the upper plate is put forward based on the forward and inverse solutions of the platform’s speed and force. The 4TPS-PS platform prototype built by the State Key Laboratory of Fluid Power Transmission and Control of China is taken as the research subject. The full reachable rotation workspace of the prototype is computed out and analyzed. The curves of maximum generalized speed and maximum generalized force of the prototype are computed out and plotted. Finally, the computing and analyzing results of the operating characteristics are confirmed through the experiment.

This paper presents a deep research on 2-DOF planar parallel mechanism during developing a new type of hybrid machine tool. The composition of this planar parallel mechanism is introduced, its direct and inverse kinematics solution equations as well as the solution equations for the speed and the acceleration are deduced, meanwhile, the jacobian matrix is obtained. The statics problems of the parallel mechanism are modeled and analyzed based on principle of virtual work, and the balancing driving force solution equation of the driving part is given. Through the solving process we can see that the direct and inverse solution equations of this mechanism have explicit expressions and convenient to realize real-time control. It forms a solid basis for the design and development of this mechanism.

SUMMARYForce control is important in robotics research for safe operation in the interaction between a manipulator and a human operator. The elasticity center is a very important characteristic for controlling the force of a manipulator, because a force acting at the elasticity center results in a pure displacement of the end-effector in the same direction as the force. Similarly, a torque acting at the elasticity center results in a pure rotation of the end-effector in the same direction as the torque. A stiffness synthesis strategy is proposed for a desired elasticity center for three-degree-of-freedom (DOF) planar parallel mechanisms (PPM) consisting of three revolute-prismatic-revolute (3RPR) links. Based on stiffness analysis, the elasticity center is derived to have a diagonal stiffness matrix in an arbitrary configuration. The stiffness synthesis is defined to determine the configuration when the elasticity center and the diagonal matrix are given. The seven nonlinear system equations are solved based on one reference input. The existence and the solvability of the nonlinear system equations were analyzed using reduced Gröbner bases. A numerical example is presented to validate the method.