Algebraic solution to forward kinematics of a 3‐DOF spherical parallel manipulator

A three degree‐of‐freedom (3‐DOF) spherical parallel manipulator consists of two tetrahedrons (pyramids). The base tetrahedron is fixed while the moving tetrahedron is rotating at the joint apex of the two tetrahedrons. This article studies the forward kinematics to a special 3‐DOF spherical parallel manipulator, where the three apical angles of the moving tetrahedron are equal to their counterparts in the base tetrahedron, respectively. The final result of the forward kinematics to this parallel manipulator is a univariate quartic polynomial equation, which has a direct algebraic solution. In addition, a special right‐angle case of the manipulator is investigated and its forward kinematics can be obtained directly. © 2001 John Wiley & Sons, Inc.     

Analysis and optimization of the 5-RPUR parallel manipulator

Many industrial applications need less than 6 degrees of freedom (DOF) to manipulate. On one hand, the parallel manipulators (PMs) with lower DOF have some advantages such as low manufacturing and control cost. On the other hand, they have more complicated kinematics. Among PMs with lower DOF, the 5-DOF PMs have particularly many industrial applications. Within the group of 5-DOF PMs, the three translational and two rotational (3T2R) type has more industrial applications than three rotational and two translational type. In this paper, we analyze and optimize the 5-RPUR PM which is a 3T2R type. The kinematic analysis is studied using the screw theory. The boundary and volume of the workspace is obtained using a geometrical method. In addition, singularity analysis is studied. Particle swarm optimization is utilized to optimize the workspace and the accuracy simultaneously, and achieve a roughly homogeneous accuracy index over the workspace. The boundary of the optimized workspace is depicted and we show that the optimized workspace is singularity free. The accuracy index of the manipulator is calculated and depicted in several cross-sections of the workspace.     

Type synthesis of 5‐DOF parallel manipulators based on screw theory

With the introduction of virtual chains to represent the motion patterns of 5‐DOF motions, a classification of 5‐DOF PMs (parallel manipulators) is proposed at first. A general method for the type synthesis of 5‐DOF PMs is then proposed based on screw theory and using the concept of virtual chains. The type synthesis of US‐equivalent PMs is presented in detail to show the application of the proposed approach. US‐equivalent PMs are the parallel counterparts of the 5‐DOF US serial manipulators. For a US‐equivalent PM, the moving platform can rotate arbitrarily about a point moving along a spherical surface. The type synthesis of legs for US‐equivalent PKCs (parallel kinematic chains), the type synthesis of US‐equivalent PKCs, as well as the selection of actuated joints of US‐equivalent PMs are dealt with in sequence. US‐equivalent PKCs with and without inactive joints are synthesized. Several US‐equivalent PMs as well as other classes of 5‐DOF PMs with identical type of legs are obtained. © 2005 Wiley Periodicals, Inc.     

A new family of hybrid 4‐DOF parallel mechanisms with two platforms and its application to a footpad device

This paper proposes a new family of 4‐degrees‐of‐freedom (DOF) parallel mechanisms with two platforms and its application to a footpad device that can simulate the spatial motions of the human foot. The new mechanism consists of front and rear platforms, and three limbs. Two limbs with 6‐DOF serial joints (P ‐S‐P‐P) are attached to each platform and are perpendicular to the base plate, while the middle limb is attached to the revolute joint that connects the front and rear platforms. The middle limb is driven by the 2‐DOF driving mechanism that is equivalent to active serial prismatic and revolute joints (P_e ‐R_e ), or prismatic and prismatic joints (P_e ‐P_e ) with two base‐fixed prismatic actuators. Since the middle limb perpendicular to the base plate has 3‐DOF serial joints (P_e ‐R_e ‐R or P_e ‐P_e ‐R), two new 4‐DOF parallel mechanisms with two platforms can generate pitch motion of each platform, and roll and heave motions (1T‐3R) or pitch motion of each platform and two translational motions (2T‐2R) at both platforms, according to the type of the 2‐DOF driving mechanism. Kinematic analyses of the 1T‐3R mechanism were performed, including inverse and forward kinematics and velocity analysis. Based on the 1T‐3R mechanism, a footpad device was designed to generate foot trajectories for natural walking. © 2005 Wiley Periodicals, Inc.     

Design and Analysis of a Novel 2T2R Parallel Mechanism with the Closed-loop Limbs

Machine Intelligence Research - This paper presents a novel four degrees of freedom (DOF) parallel mechanism with the closed-loop limbs, which includes two translational (2T) DOF and two rotational...     

Translational Parallel Manipulators: New Proposals

Translational parallel manipulators are parallel manipulators wherein the end‐effector performs only spatial translations. This paper presents a new family of translational parallel manipulators. The manipulators of this family are independent constraint manipulators. They have three limbs that are topologically identical and have no rotation singularity. The limbs of these manipulators feature five one‐degree‐of‐freedom kinematic pairs in series. Four joints are revolute pairs and the remaining one, called T‐pair, is a kinematic pair that can be manufactured in different ways. In each limb, three adjacent revolute pairs have parallel axes and the remaining revolute pair has an axis that is not parallel to the axes of the other revolute pairs. The mobility analysis of the manipulators of this new family is addressed by taking into account two different choices for the actuated pairs. One of the results of this analysis is that the geometry of a translational parallel manipulator free from singularities can be defined for a particular choice of the actuated pairs. © 2002 Wiley Periodicals, Inc.     

Forward kinematic singularity avoiding design of a Schönflies motion generator by asymmetric attachment of subchains

In most of the previous studies on parallel mechanisms (PMs), architectural design mainly relying on symmetric geometry was investigated without in-depth analysis of its performance. This work demonstrates that such a symmetric geometry of multiple subchains sometimes induces a forward kinematic singularity which degrades the overall kinematic performance of PMs within the desired workspace and claims that an asymmetric attachment of those subchains on a moving platform can effectively resolve such a singularity problem. A 4-Degree-of-Freedom (DOF) PM exhibiting Schönflies motions is examined as an example device. First, its mobility analysis and kinematic modeling via screw theory are conducted. Then a singularity analysis based on Grassmann line geometric conditions is carried out, and the forward kinematic singularities of the mechanism are identified and verified by simulations. Based on these analysis and simulations, a forward kinematic singularity-free design is suggested. To show the high potential of the device in practical applications, its output stiffness and dynamic motion capability are examined. Then a prototype is built and its motions capability is verified through experiments.     

Structural synthesis of 5 DoFs 3T2R parallel manipulators with prismatic actuators on the base

A method is presented to synthesize 5 degrees of freedom (DoFs) of 3 translational and 2 rotational (3T2R) parallel kinematic structures. This method is based on the theory of linear transformation and geometrical analysis. Central to this method is a set of novel 5 DoFs 3T2R parallel mechanisms (PMs). Based on the legs configuration, the generated mechanisms are classified. Moreover, the promising mechanisms of each class are introduced with respect to some criteria, i.e.: (a) degree of coupling between the actuators and degrees of freedom; (b) easy kinematics and control command; (c) easy construction (or low cost construction); and, (d) manufacturability. With reference to these criteria, some discussions are given on the promising mechanisms. Finally, to demonstrate the role of legs configuration in relation to the characteristics of a manipulator, the kinematic analysis of two of the introduced mechanisms is compared.     

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 Geometric Theory for Analysis and Synthesis of Sub-6 DoF Parallel Manipulators

Mechanism synthesis is mostly dependent on the designer's experience and intuition and is difficult to automate. This paper aims to develop a rigorous and precise geometric theory for analysis and synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of SE(3) and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.     

Analytical Identification of Limb Structures for Translational Parallel Manipulators

A systematic analytical method, based on the theory of screws, is presented for identification of limb structures of general and over‐constrained 3‐degree‐of‐freedom (DOF) translational parallel manipulators. Given a system of wrenches of constraint, the corresponding reciprocal basis screws are determined. Then, the joint screws of a limb are obtained by a linear combination of these basis screws. Feasible limbs that can be used for construction of translational platforms are enumerated according to the type of constraint and the number of joints making up the limbs. © 2004 Wiley Periodicals, Inc.     

具有7自由度和双球型髋关节的仿人机器人下肢运动分析与规划

提出了具有7自由度和双球型髋关节的仿人机器人下肢机构．它和传统的6自由度双足步行机构相比,具有下述两大优点．首先双球型髋关节使机器人在不增加腰部关节的情况下实现腰部的基本运动功能,使机器人能够直立行走;其次在给定腰和足部位置时,它也能和人类一样实现转动双腿的动作．本文还对该复杂机构进行了运动特性分析、运动学求解、运动规划和实验验证．     

A kinematic analysis of the space station remote manipulator system (SSRMS)

An efficient reverse analysis of three 6-degree-of-freedom (dof) subchains of the 7-dof SSRMS is presented. The first subchain is formed by locking the seventh joint. The second subchain is formed by locking the second joint, while the third subchain is formed by locking the first joint (the grounded joint is counted as the first joint in the chain). There are a maximum of eight different arm configurations in each of the three subchains, and these were determined by employing a computer-efficient algorithm, which required the rooting of only at most quadratic polynomials. The algorithms were implemented, and the SSRMS was employed in an animated environment to perform and practice a number of useful tasks for space station servicing. The locking of the second joint has the advantage in that an operator could, at the outset, choose the orientation of the plane that contains the two longest links (the upper arm and forearm) so as to avoid collisions with obstacles. However, it has the disadvantage that when the second joint angle equals 0° or 180°, the manipulator is in a singularity configuration (a singularity analysis of the SSRMS is presented in a second article). It is interesting to note that this plane can also be oriented by specifying the first joint angle. This has the distinct advantage that the plane can be oriented arbitrarily and, in this way, the singularity is avoided.     

CAT4 (Cable Actuated Truss—4 Degrees of Freedom): A Novel 4 DOF Cable Actuated Parallel Manipulator

The CAT4 (Cable Actuated Truss—4 degrees of freedom) robot is a novel, passively jointed, parallel robot utilizing six control cables for actuation. The architecture has been under development at the Queen's University Robotics Laboratory. The robot utilizes a passive jointed linkage with 18 revolute joints to constrain the end effector motion and provide the desired structural stability, restricting the end effector to 3 translational degrees of freedom (DOF) and 1 DOF for end effector pitch. This central mechanism together with winched cable actuation gives a number of important benefits for applications where the advantages of a parallel robot are required in conjunction with light weight. Six electric motor driven winches control the length of the cable actuators that extend from the top frame to points on the end effector raft and jointed linkage to create a stiff, but lightweight, actuated robot. Simulation work on the robot is presented giving the kinematics, including a computational estimate of the workspace for a specific configuration. Results of computational simulation of the motion of the manipulator and a discussion of the advantages and potential difficulties are also presented. © 2002 Wiley Periodicals, Inc.     

Design and Control of 6-DOF Mechanism for Twin-Frame Mobile Robot

A new lightweight six-legged robot that uses a simple mechanism and can move and work with high efficiency has been developed. This robot consists of two leg-bases with three legs each, and walks by moving each leg-base alternately. These leg-bases are connected to each other with a 6 degrees of freedom (DOF) mechanism. While designing this robot, the output force, velocity, and workspace of various connection mechanisms were compared, and the results showed that good performance could be achieved with a serial/parallel hybrid mechanism. The serial/parallel hybrid mechanism consists of three 6-DOF serially linked arms positioned with radial symmetry about the center of each leg-base; each leg-base is composed of two active and four passive joints. Walking experiments with this robot confirmed that this mechanism has satisfactory performance not only as a walking robot, but also as an active walking platform. Furthermore, in this robot, the entire leg-drive mechanism acts as a 6-axis force sensor, and individual sensors at the feet are not necessary. The forces and moments can be calculated from the changes in the joint angles. Experiments conducted verified that smooth contact with the ground by the swing-leg and successful switching from swing to support leg can be achieved using this force control and force measurement method.     

Intuitive Bilateral Teleoperation of a Cable-driven Parallel Robot Controlled by a Cable-driven Parallel Robot

International Journal of Control, Automation and Systems - Intuitive remote multiple degrees of freedom (DOF) robot control has distinct advantages in field robotics applications, especially for a...     

Gpc‐Based Self‐Tuning PI Controller for Speed Servo System of PMSLM

In this paper, a generalized predictive control (GPC)‐based two degrees of freedom (2 DOF) proportional integral (PI) controller is proposed for the speed servo system of a permanent magnet synchronous linear motor (PMSLM). In this new approach, based on a dynamic model of a servo system, a simplified and high‐performance GPC supplies a 2 DOF PI controller with suitable control parameters, according to the varied operating conditions. In previous studies, GPC‐based proportional integral derivative (PID) controllers have been designed using a step‐type or ramp‐type reference input. In our work, however, the speed command for PMSLM usually is required to be a trapezium‐type signal because of the limited travel range. Hence, control performance of a speed servo system using a GPC‐based 2 DOF PI controller is enhanced for tracking a trapezium‐type command. The validity and usefulness of the proposed controller are verified through simulation and experiments.     

2‐DOF discrete‐time nonlinear ℋ︁∞‐filters

In this paper, a new theory of two‐degrees‐of‐freedom (2‐DOF)‐??_∞ and certainty‐equivalent filters is presented. Exact and approximate solutions to the nonlinear ??_∞ filtering problem using this class of filters are derived in terms of discrete‐time Hamilton–Jacobi–Isaacs equations. The expressions for the filter gains are determined as functions of the filter state and the system's output in contrast to earlier results. Hence, it is shown that coupled with the additional degree‐of‐freedom, these filters are a substantial improvement over the earlier 1‐DOF case. The theory presented is also generalized to n‐DOF filters, which bore strong connections to linear infinite‐impulse response filters and hence are generalizations of this class of filters to the nonlinear setting. Simulation results are also given to show the usefulness of the new approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Inverse Dynamic Model and a Control Application of a Novel 6-DOF Hybrid Kinematics Manipulator

Kinematics with six degrees of freedom can be of several types. This paper describes the inverse dynamic model of a novel hybrid kinematics manipulator. The so-called Epizactor consists of two planar disk systems that together move a connecting element in 6 DOF. To do so each of the disk systems has a linkage point equipped with a homokinetic joint. Each disk system can be described as a serial 3-link planar manipulator with unlimited angles of rotation. To compensate singularities, a kinematic redundancy is introduced via a fourth link. The kinematic concept leads to several technical advantages for compact 6-DOF-manipulators when compared to established parallel kinematics: The ratio of workspace volume and installation space is beneficial, the number of kinematic elements is smaller, and rotating drives are used exclusively. For a singularity-robust control-approach, the inverse dynamic model is derived using the iterative Newton–Euler-method. Feasibility is shown by the application of the model to an example where excessive actuator velocities and torques are avoided.     

一种基于高压水射流的金属板材柔性渐进成形技术

本文提出了一种新型的金属板材无模成形方法,即高压水射流柔性渐进成形方法,并基于此方法设计出一套五轴成形装置,其中喷嘴具有二个旋转自由度,工作台具有三个平动自由度,具有很好的柔性,非常适合多品种小批量产品的生产和新产品的试制。对高压水射流柔性渐进成形装置的各个子系统进行了详细的介绍,并对成形过程提出了一种新的仿真分析方法,将比较复杂的流固耦合问题,简化为加载等效压强的方法。最后通过单点水柱成形的仿真分析,揭示射流压力和板厚对金属板材成形性能的影响。