Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

In order to obtain direct solutions of parallel manipulator without divergence in real time,a modified global Newton-Raphson(MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom(DOF) parallel manipulator.Based on geometrical frame of parallel manipulator,the highly nonlinear equations of kinematics were derived using analytical approach.The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration.The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation.The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed.Applying the MGNR algorithm,the real generalized pose of moving platform is solved by using the set of given positions of actuators.The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy(1×10-9 m in linear motion and 1×10-9 rad in angular motion),even the initial guess value is far from the root.

CONCISE SOLUTION OF FORWARD KINEMATICS ANALYSIS OF PARALLEL MECHANISM IN 6-SPS SIMILAR PLATFORM

The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.

FORWARD KINEMATICS ANALYSIS FOR A NOVEL 5-DOF PARALLEL MECHANISM USING TETRAHEDRON CONFIGURATIONS

Forward kinematics analysis of a novel 5-DOF parallel mechanism using tetrahedron configurations is presented. Such mechanism is suitable to many tasks requiring less than 6 DOFs. It consists of a movable platform connected to the base by five identical 6-DOF active limbs plus one active limb with its DOF being exactly the same as the specified DOF of the movable platform, which leads to its legs＇ topology 4-UPS/UPU. Based on the tetmhedron geometry, both closed-form solution with an extra sensor and numerical method using iterative algorithm are employed to obtain the forward kinematics solutions of the mechanism. Compared with the conventional methods, the proposed closed-form solution has the advantages in automatically avoiding unnecessary complex roots and getting a unique solution for the forward kinematics. Finally, an example shows that the proposed numerical algorithm is so effective that it enables a real-time forward kinematics solution to be achieved and the initial value can be chosen easily.

Fast Numerical Solution to Forward Kinematics of General Stewart Mechanism Using Quaternion

The forward kinematics of the general Stewart mechanism is studied and a fast numerical method is presented.Quaternion is utilized to model the forward kinematics and the equations are merely a system of quadratic ones.The numerical method is a nice simplification of the Newton-Raphson method when applied to this system.A simulation of the movement control of the Stewart mechanism is accomplished,confirming the effectiveness of the proposed algorithm in real-time conditions.

A Mixed Real-time Algorithm for the Forward Kinematics of Stewart Parallel Manipulator

Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Firstly taking advantage of simpleness of inverse kinematics, the forward kinematics is transformed to an optimal problem. Immune evolutionary algorithm is employed to find approximate solution of this optimal problem in manipulator＇s workspace. Then using above solution as iterative initialization, a speedy numerical iterative scheme is proposed to get more precise solution. In the manipulator running course, the iteration initialization can be selected as the last period position and orientation. Because the initialization is closed to correct solution, solving precision is high and speed is rapid enough to satisfy real-time requirement. This mixed forward kinematics algorithm is applied to real Stewart parallel manipulator in the real-time control course. The examination result shows that the algorithm is very efficient and practical.

;ast forward kinematics algorithm for real-time and ligh-precision control of the 3-RPS parallel mechanism

A new forward kinematics algorithm for the mechanism of 3-RPS （R： Revolute; P： Prismatic; S： Spherical） parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10 6. In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.

Forward Position Analysis of 5-DOF Parallel Mechanism

A systematic method for the forward kinematics of a five degrees of freedom （5-DOF） parallel mechanism with the legs＇ topology 4-UPS/UPU, is developed. Such mechanism is composed of a movable platform connected to the base by four identical 6-DOF active limbs plus one active limb with its DOF being exactly the same as the specified DQF of the movable platform. Three translational and two rotational DOFs can be achieved. Firstly, a set of polynomial equations of forward position analysis is formulated based on the architecture of the mechanism. Then the system of equations is degraded from five-dimensional to three-dimensional by means of analytic elimination. Method of least squares and Gauss-Newton algorithm are used to construct the objective function and to solve it, respectively. Example shows that through 4-time iteration within 16 ms the ohjective, function converaes to the provided error tolerance. 10^-4.

Analysis of kinematic and singular configurations of an asymmetrical parallel mechanism

The forward kinematics and singularity configuration of an asymmetrical parallel mechanism with three translational degrees of freedom were analyzed. By establishing the position equations of the mechanism and obtaining the forward solutions, a better decoupling of the mechanism was proved. Based on the Jacobi velocity transfer matrix, the possible singularity configurations were studied and the methods avoiding these configurations discussed. Although improving the rigidity, the 4R structures in the mechanism also resulted in new singularity configurations. By analysis of a feasible instance, this kind of parallel mechanism can avoid all singularity configurations. Meanwhile, it was proved that the design of structure parameters and the choice of inputs range are important for rigidity and stability of parallel mechanisms.

Design considerations of high precision 6-HTRT parallel manipulator

Describes a new architecture of a parallel robot with six degrees of freedom and focuses on improving orientation accuracy of movable platform in mechanism, error correction and control methods. A set of formulations about inverse kinematics, Jacobin matrix, and forward kinematics for the high precision 6-HTRT parallel robots is presented. The analysis of errors existing in the manipulator is discussed and a novel approach for error correction is advanced. By DSP technique, inverse kinematics is solved in real time conditions with high precision and the hardware control system is given. The experimental results demonstrate the effectiveness of the proposed technique.

Research of 6-DOF Serial-Parallel Mechanism Platform for Stability Training of Legged-Walking Robot

The concept of legged-robot stability training with a training platform is proposed and a serial-parallel mechanism platform with 6 degrees of freedom is designed for this target. The designed platform is composed of 4-DOF parallel mechanism with spherical joints and prismatic pairs,and 2-DOF serial mechanism with prismatic pairs. With this design,the platform has advantages of low platform countertop,big workspace,high carrying capacity and high stiffness. On the basis of DOF analysis and computation of space mechanism,weight supporting auxiliary mechanism and raceways-balls supporting mechanism are designed,so as to improve the stiffness of designed large platform and payload capacity of servo motors. And then the whole structure design work of the platform is done. Meanwhile,this paper derives the analytical solutions of forward kinematics, inverse kinematics and inverse dynamics. The error analysis model of position and orientation is established. And then the simulation is done in ADAMS to ensure the correctness and feasibility of this design.

Bogie's Rotational Resistance Coefficient Analysis Based on Novel Parallel Mechanism

In this paper,a novel parallel mechanism which can be used to evaluate body-to-bogie yawtorque is proposed.It can satisfy experimental testing for rotation resistance coefficient(RRC) with various types of bogies,different rotational speeds,and different states of air spring.Aiming at the problem that computing speed of Newton iterative method for solving rotational angle is incompetence to meet the real-time requirements,and also that other methods adopting physical device such as laser displacement sensor to solve rotational angle possess larger measurement error,the analytical techniques method used for solving rotational angle is presented.Finally,by using the upper-single-6-DOF motion platform as an authentic urging mean to simulate a real vehicle,the test was carried out under the speeds of 0.2 and 1.0(°)/s,with the air spring at the inflated and deflated states,respectively.The results showthat the RRC of the bogie under various conditions is less than 0.06,which meets the standard requirement EN-14363.It was also found that the speed of vehicles moving along curves and the state of air spring were key factors influencing the RRC.The feasibilities of this model and test method are verified in this study.

Research on Optimizing Numerical Calculation of Posture Equations based on Six DOF Stewart Platform

The paper study position positive solution method based on 6-TPS parallel mechanism, and establish general kinematics model of 6-TPS parallel mechanism, gives the numerical method of positive solution based on a kind of position, deduced the forward position solution iteration format, and use MATLAB for the 6-TPS parallel mechanism kinematics to simulation, results show that solving program has stability, fast. effective.

Error Analysis of Three Degree-of-Freedom Changeable Parallel Measuring Mechanism

A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.

A modified forward and backward reaching inverse kinematics based incremental control for space manipulators

Forward and backward reaching inverse kinematics(FABRIK)is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix.Based on FABRIK,this paper presents an incremental control scheme for a free-floating space manipulator consists of revolute joints and rigid links with the consideration of joint constraints and dynamic coupling effect.Due to the characteristics of FABRIK,it can induce large angular movements on specific joints.Apart from that,FABRIK maps three dimensional(3D)problem into two dimensional(2D)problem by a simple geometric projection.This operation can cause infinite loops in some cases.In order to overcome these issues and apply FABRIK on space manipulators,an increments allocation method is developed to constrain the angular movements as well as to re-orient the end-effector.The manipulator is re-positioned based on the momentum conservation law.Instead of pure target position tracking,the orientation control of the end-effector is also considered.Numerical simulation is performed to testify and demonstrate the effectiveness and reliability of the proposed incremental control approach.

Shape Sensing for Single-Port Continuum Surgical Robot Using FewMulticore Fiber Bragg Grating Sensors

We proposed a method for shape sensing using a few multicore fiber Bragg grating (FBG) sensors ina single-port continuum surgical robot (CSR). The traditional method of utilizing a forward kinematic model tocalculate the shape of a single-port CSR is limited by the accuracy of the model. If FBG sensors are used forshape sensing, their accuracy will be affected by their number, especially in long and flexible CSRs. A fusionmethod based on an extended Kalman filter (EKF) was proposed to solve this problem. Shape reconstructionwas performed using the CSR forward kinematic model and FBG sensors, and the two results were fused usingan EKF. The CSR reconstruction method adopted the incremental form of the forward kinematic model, whilethe FBG sensor method adopted the discrete arc-segment assumption method. The fusion method can eliminatethe inaccuracy of the kinematic model and obtain more accurate shape reconstruction results using only a smallnumber of FBG sensors. We validated our algorithm through experiments on multiple bending shapes underdifferent load conditions. The results show that our method significantly outperformed the traditional methodsin terms of robustness and effectiveness.

Wearable sensors for 3D upper limb motion modeling and ubiquitous estimation

Human motion capture technologies are widely used in interactive game and learning, animation, film special effects, health care, and navigation. Because of the agility, upper limb motion estimation is the most difficult problem in human motion capture. Traditional methods always assume that the movements of upper arm and forearm are independent and then estimate their movements separately; therefore, the estimated motion are always with serious distortion. In this paper, we propose a novel ubiquitous upper limb motion estimation method using wearable microsensors, which concentrates on modeling the relationship of the movements between upper arm and forearm. Exploration of the skeleton structure as a link structure with 5 degrees of freedom is firstly proposed to model human upper limb motion. After that, parameters are defined according to Denavit-Hartenberg convention, forward kinematic equations of upper limb are derived, and an unscented Kalman filter is invoked to estimate the defined parameters. The experimental results have shown the feasibility and effectiveness of the proposed upper limb motion capture and analysis algorithm.