Singularity-free path planning for the Stewart platform manipulator

This paper addresses the problem of singularity-free path planning for the six-degree-of-freedom parallel manipulator known as the Stewart platform manipulator. Unlike serial manipulators, the Stewart platform possesses singular configurations within the workspace where the manipulator is uncontrollable. An algorithm has been developed to construct continuous paths within the workspace of the manipulator by avoiding singularities and ill-conditioning. Given two end-poses of the manipulator, the algorithm finds out safe (well-conditioned) via points and plans a continuous path from the initial pose to the final one. When the two end-poses belong to different branches and no singularity-free path is possible, the algorithm indicates the impossibility of a valid path. A numerical example has also been presented as illustration of the path planning strategy.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

An algebraic formulation of static isotropy and design of statically isotropic 6-6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration. (C) 2008 Elsevier Ltd. All rights reserved.

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

A canonical formulation of the direct position kinematics problem for a general 6-6 stewart platform

This paper deals with the direct position kinematics problem of a general 6-6 Stewart platform, the complete solution of which is not reported in the literature until now and even establishing the number of possible solutions for the general case has remained an unsolved problem for a long period. Here a canonical formulation of the direct position kinematics problem for a general 6-6 Stewart platform is presented. The kinematic equations are expressed as a system of six quadratic and three linear equations in nine unknowns, which has a maximum of 64 solutions. Thus, it is established that the mechanism, in general, can have up to 64 closures. Further reduction of the system is shown arriving at a set of three quartic equations in three unknowns, the solution of which will yield the assembly configurations of the general Stewart platform with far less computational effort compared to earlier models.

A near-singular, flexure jointed, moment sensitive Stewart platform based fore-torque sensor

A force-torque sensor capable of accurate measurement of the three components of externally applied forces and moments is required for force control in robotic applications involving assembly operations. The goal in this paper is to design a Stewart platform based force torque sensor at a near-singular configuration sensitive to externally applied moments. In such a configuration, we show an enhanced mechanical amplification of leg forces and thereby higher sensitivity for the applied external moments. In other directions, the sensitivity will be that of a normal load sensor determined by the sensitivity of the sensing element and the associated electronic amplification, and all the six components of the force and torque can be sensed. In a sensor application, the friction, backlash and other non-linearities at the passive spherical joints of the Stewart platform will affect the measurements in unpredictable ways. In this sensor, we use flexural hinges at the leg interfaces of the base and platform of the sensor. The design dimensions of the flexure joints in the sensor have been arrived at using FEA. The sensor has been fabricated, assembled and instrumented. It has been calibrated for low level loads and is found to show linearity and marked sensitivity to moments about the three orthogonal X, Y and Z axes. This sensor is compatible for usage as a wrist sensor for a robot under development at ISRO Satellite Centre.

Mathematical modelling of linear motion error for Hexarot parallel manipulators

Hexarot is a robotic manipulator that belongs to the family of axis symmetric parallel mechanisms. The robot is able to move the robot platform or tool center point in six degrees of freedom (DOF). This paper presents the kinematics model of the robot including the inverse and forward kinematics, and its time derivatives. Then using the kinematics formulations, investigation of the nonlinear motion of the Hexarot robot for a desired linear motion path is performed. For this purpose, the concept of curvature of the robot path is used for measuring the nonlinearity of the actual motion of the robot. The nonlinear motion error of the robot is analyzed for the scenario where the platform moves on a linear path between two arbitrary points of the robot workspace. The effects of different parameters on the nonlinear motion error of the mechanism are demonstrated and strategies for motions with low error values are proposed.

Design and Development of 3-DOF Modular Micro Parallel Kinematic Manipulator

This paper presents the research and development of a 3-legged micro Parallel Kinematic Manipulator (PKM) for positioning in micro-machining and assembly operations. The structural characteristics associated with parallel manipulators are evaluated and the PKMs with translational and rotational movements are identified. Based on these identifications, a hybrid 3-UPU (Universal Joint-Prismatic Joint-Universal Joint) parallel manipulator is designed and fabricated. The principles of the operation and modeling of this micro PKM is largely similar to a normal size Stewart Platform (SP). A modular design methodology is introduced for the construction of this micro PKM. Calibration results of this hybrid 3-UPU PKM are discussed in this paper.

An algebraic formulation of exact force-, moment-isotropy in spatial parallel manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions.We use the force and moment transformation matrices separately,and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation has been applied to a class of Stewart platform manipulators. We obtain multi-parameter families of isotropic manipulator analytically. In addition to computing the isotropic configurations of an existing manipulator,we demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

一种Stewart结构六维力/力矩传感器参数辨识研究

介绍了一种大量程Stewart结构六维力/力矩传感器系统.建立了传感器力/力矩测量数学模型,构建了基于运动学逆解的优化目标函数.提出了一种新的参数标定法,称作分支轮换标定法.基于所研发的六维力/力矩传感器系统进行了实验研究,实验结果表明分支轮换法可以有效地辨识出传感器的结构参数,提高了测量精度.该方法可用于类似结构的六维力/力矩传感器参数标定.

大射电望远镜精调Stewart平台工作空间分析

针对大射电望远镜精调Stewart平台的五自由度运动特性,采用快速极坐标搜索法确定了五自由度大射电望远镜精调Stewart平台的工作空间.通过实例分析验证了所提出的工作空间分析方法的有效性.为大射电望远镜馈源轨迹跟踪实现和精调Stewart平台的设计奠定了坚实的基础.

基于四自由度并联机构的数控机床研究

介绍一种基于混合型四自由度并联平台机构开发的五坐标并联机床 .由于其独特的机构设计 ,与基于 Stewart平台的并联机床相比 ,X方向的进给运动与运动平台分离 ,改由工作台单独进给 ,因而其工作空间成倍增大 .采用龙门框架结构和滚珠丝杠支承方案使机床获得更高的刚度 .给出了该机床运动学逆解 ,控制系统采用基于 PC的数控系统进行五轴联动控制

基于Stewart平台六维力传感器的分区静态标定方法

基于Stewart平台的六维力传感器具有结构紧凑、刚度大、量程宽等特点,它在工业机器人、空间站对接等领域具有广泛的应用前景。好的标定方法是正确使用传感器的基础。由于基于Stewart平台的六维力传感器是一个复杂的非线性系统,所以采用常规的线性标定方法必将带来较大的标定误差从而影响其使用性能。标定的实质是,由测量值空间到理论值空间的映射函数的确定过程。由函数逼近理论可知,当只在已知点集上给出函数值时,可用多项式或分段多项式等较简单函数逼近待定函数。基于上述思想,本文将整个测量空间划分为若干连续的子测量空间,再对每个子空间进行线性标定,从而提高了整个测量系统的标定精度。实验分析结果表明了该标定方法有效。

并联Stewart机构位姿误差分析

从并联机构与串联机构的运动学等效 ,并联机构本身特征与并联机构实际工作空间出发 ,考虑各分支末端误差对最终运动平台末端误差的影响 ,提出了并联机构位姿误差放大因子分析法·依据位姿误差放大因子具有对误差定量分析的特点 ,该分析方法既可用于机构参数优化 ,又可用于结构精度设计· 最后 ,给出了一个实例说明本方法的有效性·