OPTIMAL MECHANISM DESIGN AND DYNAMIC ANALYSIS OF A 3‐LEG 6‐DOF LINEAR MOTOR BASED PARALLEL MANIPULATOR

This paper presents the optimal mechanism design and dynamic analysis of a prototype 3‐leg 6‐DOF (degree‐of‐freedom) parallel manipulator. Inverse kinematics, forward kinematics, inverse dynamics and working space characterizing the platform motion are derived. In the presented architecture, the base platform has three linear slideways individually actuated by a synchronous linear servo motor, and each extensible vertical link connecting the upper and base platforms is actuated by an inductive AC servo motor. The linear motors contribute high‐speed movements to the upper platform. This kind of architecture using hybrid (linear and AC) motors yields high level performance of motions, especially in the working space. The novel result of maximal working angles is the significant contribution of this architecture. The Taguchi Experimental Method is applied to design the optimal mechanism of the platform system, and the result is used as the actual data to build this system.     

Reconfigurability and unified kinematics modeling of a 3rTPS metamorphic parallel mechanism with perpendicular constraint screws

This paper investigates reconfigurability and unified analytical kinematics analysis of a new 3rTPS metamorphic parallel mechanism consisting of three reconfigurable rTPS limbs in perpendicular base planes. Constraint screw systems show that in one phase the rTPS limb has no constraint to the platform and in the other phase obtained by altering the reconfigurable Hooke joint, it provides a constraint force. The two phases of the limb qualify the 3rTPS metamorphic parallel mechanism to have four topologies with ability of mobility change among 3R (three rotations), 3R1T (three rotations one translation), 3R2T and mobility 6. By considering the difference of the two phases of the limb, a unified kinematics modeling is proposed based on the actuation scheme analysis by taking one phase as a special case of the other. Following this, a unified kinematics modeling of the 3rTPS metamorphic parallel mechanism is obtained by covering all its four topologies. Both inverse and forward kinematics analysis are solved analytically and numerical examples confirm these theoretical results.     

Hybrid head mechanism of the groundhog-like mine rescue robot

Since mining accidents severely threaten production safety, robotic assistant systems can play an important role by searching and rescuing survivors in hostile underground environments. Accordingly, this paper focuses on the design, modeling and optimization of a 4UPS+PU spatial hybrid manipulator, which serves as the dexterous head section of a quadrupedal, groundhog-like mine rescue robot. This biologically inspired mechanism has three degrees of freedom (DOF), one translation and two rotations. Additionally, a passive leg is connected to both centers of the base and the moving platform in order to constrain undesirable motion. In order to evaluate the operational capacity, an analysis of the mobility and the inverse kinematics are conducted. The reachable workspace is generated with a boundary-searching discretization approach, and the local and global performance atlas, including stiffness and dexterity, are investigated. The multi-population evolution of structural and behavioral parameters is implemented to seek the optimal dexterity of the hybrid head mechanism.     

Kinematic design of a six-DOF parallel-kinematics Machine with decoupled-motion architecture

The design of a new six-degree-of-freedom (6-DOF) parallel-kinematics machine (PKM) has been proposed. Different from the conventional Stewart-Gough platform which has six extensible legs, the new PKM employs three identical RPRS legs to support the moving platform. Since all joint axes, excluding the three spherical joints at the leg ends, are parallel to each other and perpendicular to the base plane, this 6-DOF PKM presents a promising platform structure with decoupled-motion architecture (DMA) such that translation in a horizontal plane and rotation about a vertical axis are driven by the three active revolute joints, while translation in the vertical direction and rotation about horizontal axes are driven by the three active prismatic joints. As a result, this 6-DOF 3RPRS PKM with DMA has simple kinematics, large cylindrical reachable workspace, and high stiffness in the vertical direction. These features make it appropriate for light machining and heavy parts assembly tasks. Because of the DMA, a projection technique is employed for its kinematics analysis. By projecting the manipulator onto horizontal directions and vertical planes, the kinematics issues such as the displacement, singularity, and workspace analysis are significantly simplified.     

The application of the Stewart platform in large spherical radio telescopes

For the requirement of trajectory tracking of large spherical radio telescopes, a large fine tuning platform based on the Stewart platform is presented in this paper. The mathematical model for kinematics control is developed with coordinate transformation, and a dynamic analysis is made using a Jacobian matrix. Furthermore, the singularity analysis of the designed platform is also made using the determinant of the Jacobian matrix, which has built a solid base for the tracking control. The kinematics accuracy is obtained by position vector analysis. These results have shown the validity of the designed fine tuning platform for the feed source trajectory tracking control of large spherical radio telescopes. ©2000 John Wiley & Sons, Inc.     

Combined Inverse Kinematic and Static Analysis and Optimal Design of a Cable-Driven Mechanism with a Spring Spine

Abstract

A special humanoid neck with low motion noise requirements yields a cable-driven parallel mechanism to imitate the rotational motion of a human neck. The fixed base and moving platform of the mechanism are connected by four cables and a column compression spring. The four cables are actuated separately, while the spring can support weight on the moving platform. Although similar mechanisms exist in the literature, the analysis of them is scarce because a flexible spring instead of a rigid kinematic chain is used as the spine. With the spring’s lateral buckling motion, a new approach must be adopted to solve the kinematics. In this paper, we propose a method that combines the kinematics with the statics to solve them simultaneously. The configuration of the moving platform is parameterized with four parameters, one of which is considered as parasitic motion. Using the spring’s lateral buckling equation, we can obtain the parasitic motion and solve the inverse position problem. The optimal design for cable placements is then performed to minimize the actuation force. The method in this paper provides a novel way to analyze parallel mechanisms with a spring spine and it can be applied to other mechanisms with flexible spines.     

Motion analysis of a tripod parallel mechanism

A tripod parallel mechanism consists of three links of fixed length and a rigid platform, and these are connected by revolute joints. The platform can achieve sixdegrees-of-freedom (6-DOF) motion by the coordinated movement of the bottom ends of the three links on a horizontal plane. This mechanism has advantages over the more common six extendible parallel manipulators. It has a much larger work space and a simple structure. In this article, we show that the vector analysis for this tripod parallel mechanism and the derivation of the positions of the three bottom ends of the links in an arbitrary attitude of platform can be found by inverse kinematics and the conditions of geometrical constraint. Then, by a numerical simulation, the trajectories of the bottom ends of the three links are shown.     

A Novel Six Degrees-of-Freedom Parallel Robot for MEMS Fabrication

This paper introduces a new architecture of a six degrees-of-freedom parallel robot suitable for microelectromechanical systems (MEMS) fabrication. The robot consists of only revolute joints for the passive joints, and linear actuators located at the base for the active ones, both of which are easier to manufacture in MEMS technology. The hybrid kinematic structure contains three single-loop submechanisms connected in parallel to the moving platform. The solutions of the inverse and direct kinematics problems are presented     

3-RRRT并联机器人位置正向求解研究

研究一种3-RRRT型并联机器人机构的运动学正向求解方法。根据3-RRRT型并联机器人机构特点以及关节运动的取值范围,提出了以并联机器人支链中支杆的方向余弦和动平台绝对位置坐标为系统的广义坐标的方法,并详细地推导了3-RRRT型并联机器人运动学模型,通过进一步消除中间变量的方法最终获得了易于正、逆运动学求解的只包含3个驱动关节坐标与动平台3个绝对位置坐标的约束方程组。最后,运用基于Moore—Penwse广义逆的牛顿迭代格式编制了MATLAB运动学正向求解程序,并进行了运动学正向求解数值仿真,结果表明求解程序快速有效。     

Mobility analysis and kinematics of the semi-general 2(3-RPS) series-parallel manipulator

This work reports on the kinematics of a series-parallel manipulator built with two zero-torsion tangential parallel manipulators assembled in series connection. Although this mechanism has been widely studied, there are some topics that must be revised, e.g. the mobility analysis here reported shows that the robot under study is not precisely a six degrees of freedom spatial mechanism as it has been commonly considered. Furthermore, the traditional hexagonal coupler platform is replaced with a three-dimensional platform which yields a mechanism with a more general topology. The forward and inverse displacement analyses of the robot are obtained in semi-closed form solutions based on simple closure equations which are generated upon the coordinates of three points embedded to the moving platform while the input–output equations of velocity and acceleration of the semi-general series-parallel manipulator are easily derived by resorting to reciprocal-screw theory. A case study is included in order to show the application of the method of kinematic analysis.     

基于牛顿-欧拉方法的6-PUS并联机构刚体动力学模型

用牛顿—欧拉方法建立了 6 PUS并联机构的动力学模型 .为使动力学模型包含所有构件的重力和惯性力 ,以该并联机构的支链为研究对象 ,用D H方法建立了各构件的坐标系 ,推导出了支链运动学逆解的解析解 ,并给出了动平台的速度、加速度与各构件速度、加速度之间的映射关系 .然后 ,以动平台为研究对象导出了 6 PUS并联机构的动力学模型 ,并给出了动平台做圆周平动时各驱动力的变化曲线 ,为该类机构的动力学分析奠定了基础 .     

Analtical- form direct kinematicefor the second scheme of a 5–5 general-geometry fully parallel manipulator

This article presents the direct kinematics of a 6 degrees of freedom fully parallel manipulator that features five connection points on both base and platform. The considered leg arrangement is one of the two possible, the other having been referred to in a previous paper. The base and platform have a general geometry, i.e., the connection points are not bound to lie on planes. The direct kinematics is solved in analytical form, which allows determination of every possible solution. After a suitable set of five equations in five unknowns has been laid down, and an original elimination procedure applied, a final polynomial equation of the 24th order is found whose 24 solutions correspond to as many assembly configurations for the considered fully parallel manipulator. A case study is reported. © 1995 John Wiley & Sons, 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.     

Forward kinematics of a class of parallel (Stewart) platforms with closed-form solutions

This article studies the geometrical condition for closed-form solutions of forward kinematics of parallel platforms. It is shown that closed-form solutions are available if 1 rotational degree of freedom (dof) of the moving platform is decoupled from the other 5 dof. Geometrically, this condition is satisfied when five end-points at the moving platform (or at the base) are colinear. A general case that these five points do not coincide with each other is studied first and is shown to have 16 possible closed-form solutions. The variations of parallel platforms that satisfy the above-mentioned geometrical condition are then discussed. Some of them have the additional feature that the three rotational dof are fully decoupled from the 3 translational dof and their closed-form solutions are further simplified. One particular case has extremely simple forward kinematics and could be used as an alternative to the Stewart platform.     

Spherically actuated platform manipulator

This article presents the inverse and forward pose and rate kinematics solutions for a novel 6‐DOF platform manipulator, actuated by two base‐mounted spherical actuators. The moving platform is connected to the fixed base by two identical spherical‐prismatic‐universal serial chain legs. The S‐joint is active, and the remaining two joints in each chain are passive. An analytical solution is presented for the inverse pose problems, a semi‐analytical solution is presented for the rate problems, and the numerical Newton–Raphson technique is employed to solve the forward pose problem. Unfortunately, the passive joint variables cannot be ignored in the kinematics solutions as they can for the Gough–Stewart platform. Examples are presented and hardware has been built, using two Rosheim Omni‐Wrists on loan from NASA as the spherical actuators. © 2001 John Wiley & Sons, Inc.     

Conceptual design and analysis of the 2T1R mechanism for a cooking robot

This paper deals with the design and analysis of a two-translation and one-rotation (2T1R) mechanism for a novel cooking robot. Firstly the motions involved in stir-fry, the most representative operation in the cooking processes used in Chinese cuisine, are analyzed in details. Then the featured motions are decomposed into four main movements that are used as a design base for a wok motion mechanism. Several three-degrees-of-freedom (DOF) parallel manipulators are considered. From these, a 2T1R mechanism is selected as an ideal candidate. A 4-DOF (2T1R+1T) cooking robot is constructed by combining the 2T1R parallel manipulator with a 1-DOF linear feed mechanism. It is shown that the combined 4-DOF robot can perform the required cooking operations, particularly the stir-fry. The analysis conducted on the proposed 2T1R parallel manipulator includes inverse kinematics, forward kinematics, the velocity analysis, the constant orientation workspace, and the total orientation workspace. A prototype of the cooking robot is developed. The experiments verify that the proposed cooking robot is suitable for performing the required operations.     

Synthesis of the forward kinematics problem algebraic modeling for the general parallel manipulator: displacement-based equations

This paper closes a triptic to address the issue of the forward kinematics problem (FKP) aimed at certified solving with an exact algebraic method. This solving method was described in the first article published in Advanced Robotics. The second one investigated the formulation specifically applied to the planar parallel manipulators. This third paper is the logical one in the footsteps of the formersones, since it continues the formulation analyses and brings them to the general spatial parallel manipulator. Hence, this paper focuses on the displacement-based equation systems. This paper is the first one to present a synthesis on forward kinematics modeling focusing on finding an optimal mathematical formulation based on the displacement-based equation systems. The majority of parallel manipulators in applications can be modeled by the 6-6 hexapod or so-called Gough platform which is constituted by a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two revolute or Cardan joints. Again, in order to implement algebraic methods, the parallel manipulator kinematics shall be formulated as polynomial equations systems where the equation number is at least equal to the unknown numbers. Six geometric formulations were derived. The selected algebraic proven method is implementing Gröbner bases from which it constructs an equivalent univariate polynomial system. The resolution of this last system exactly determines the real solutions which correspond to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. Several instantiations shall be computed in order to select the model which leads to the FKP resolution with the lowest response times and smaller file sizes. It was possible to reject three modelings leading to bad performances or resolution failure. It was possible to determine one formulation where the solving computations were definitely better than the others.     

Dynamics analysis of the Star parallel manipulator

Matrix relations in kinematics and dynamics of the Star parallel manipulator are established in this paper. The prototype of the manipulator is a three-degree-of-freedom mechanism, which consists of a system of parallel kinematical chains connecting to a moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robot’s link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Recursive formulae offer expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model.     

基于LabVIEW的机器人运动算法实现与验证平台

本文提出了一种在LabVIEW中搭建的机器人运动算法和参数的验证平台,以小型五轴机器人为例,实现对其 进行D-H参数定义、逆向运动学算法验证、轨迹规划、实时运动仿真和实体控制的功能。     

Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace

In recent years, nanotechnology has been developing rapidly due to its potential applications in various fields that new materials and products are produced. In this paper, a novel macro/micro 3-DOF parallel platform is proposed for micro positioning applications. The kinematics model of the dual parallel mechanism system is established by the stiffness model with individual wide-range flexure hinge and the vector-loop equation. The inverse solutions and parasitic rotations of the moving platform are obtained and analyzed, which are based on a parallel mechanism with real parameters. The reachable and usable workspace of the macro motion and micro motion of the mechanism are plotted and analyzed. Finally, based on the analysis of parasitic rotations and usable workspace of micro motion, an optimization for the parallel manipulator is presented. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for the dual parallel mechanism in order to achieve the features of both larger workspace and higher motion precision.