Inverse Dynamics of A 3-DOF Parallel Mechanism Based on Analytical Forward Kinematics

For the development of a parallel mechanism(PM),it is necessary to establish a dynamic model which can accurately meet the requirements of real-time control.Compared with the general dynamic analysis model based on the inverse kinematics,the dynamic analysis model based on the forward kinematics has the advantage of low-complexity.In this paper,a new type of 3-DOF PM with analytical forward displacement analysis is proposed.Different from the general dynamic analysis based on the inverse kinematics,the displacement,velocity and acceleration equations of the PM are established and solved by forward kinematics.The inverse dynamic equation of the PM is constructed and solved by analyzing the forces on each link and based on Newton-Euler method.Then the theoretical results of an example are compared with the simulation results,which shows that the simulation results are basically consistent with the theoretical results.And the maximum error of the driving force of each pair is 1.32%,5.8%and 5.2%,respectively,which verifies the correctness of the dynamic model.The PM has a potential application prospect in the grasping,spraying and picking of workpieces.The research results of this paper provide a theoretical basis for the design,manufacture and application of the PM.

Kinematics and Dynamics Analysis of a Quadruped Walking Robot with Parallel Leg Mechanism

It is desired to require a walking robot for the elderly and the disabled to have large capacity,high stiffness,stability,etc.However,the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function.Therefore,Improvement of enhancing capacity and functions of the walking robot is an important research issue.According to walking requirements and combining modularization and reconfigurable ideas,a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed.The proposed robot can be used for both a biped and a quadruped walking robot.The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized.The results show that performance of the walking robot is optimal when the circumradius R,r of the upper and lower platform of leg mechanism are 161.7 mm,57.7 mm,respectively.Based on the optimal results,the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory,and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed,which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process.Besides laying a theoretical foundation for development of the prototype,the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.

Kinematics and dynamics analysis of a 3-7R parallel decoupling mechanism

One kind of movable-pair analysis method is adopted to analyze the configuration of a 3-7R （revolute-pair） parallel decoupling mechanism, and the mechanism＇s characteristics are summarized. The mechanism has three orthogonal distributional branch-chains, and all movable pairs are rotational joints. The movable platform of the mechanism has x, y, z translational decoupling directions. Furthermore, in order to verify the mechanism＇s decoupling characteristics, the mechanism＇s kinematics analysis is solved, and the mechanism＇s direct/inverse kinematics model, input/output velocities and accelerations are deduced, which confirm its decoupling movement characteristics. Finally, one kind of mechanism link decomposed-integrated approach is adopted, and the mechanism＇s dynamics model is completed with the Lagrange method, which also proves its decoupling force characteristics. All of these works provide significant theory for the further study of the mechanism＇s control strategy, design, path planning etc.

Analysis and Simulation of Kinematical Performances of Two Kinds of Parallel Mechanisms Based on the Plane Sprayer

Two kinds of 2-dof parallel mechanisms are proposed in this paper which can be used as the actuator for the plane sprayer. The direct and inverse kinematics solutions of the two kinds of mechanisms are derived on the end operating point and two workspaces are analyzed and compared. The kinematics models of the end operating point of two mechanisms are simulated by Matlab examples obtaining variation of kinematics parameters of these two mechanisms. The research of this paper provides the basis for the selection of mechanism, trajectory planning of the end operating point on the sprayer and often some practical value for trajectory analysis and structure design of the plane sprayer.

Closed-form dynamics of a hexarot parallel manipulator by means of the principle of virtual work

In this research,a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work.For the first time,a closed form of the mathematical formulation of the standard dynamic model is presented for this class of mechanisms.An efficient algorithm for solving this closed-form dynamic model of the mechanism is developed and it is used to simulate the dynamics of the system for different trajectories.Validation of the proposed model is performed using SimMechanics and it is shown that the results of the proposed mathematical model match with the results obtained by the SimMechanics model.

A Tentative Study on Dynamics of a New Parallel NC Machine Tool with Long Travel, Large Rotating Angle and High Moving Speed

In view of the structure of traditional five-coord in ate machine tool, the work-piece and machine tool often move along their respec tive guides simultaneously on the whole. In this kind of machine structure, the total mass of moving parts including work-pieces, fixtures, rotating table, wor king table and so on is often very large. Besides, the elastic reform of transmi ssion and the viscous friction force of the guide can not be ignored. As a resul t, the machine tool can not move with high velocity and acceleration, and can no t meet the needs of modern fast and efficient production. The emergence of virtual-axis machine tool has provided a new approach for the solution of the above problems. The kernel of the virtual-axis machine tool is the parallel mechanism. So far, research of parallel mechanism in the world has achieved many results and various applied equipments based on parallel mecha nism have been worked out, but the research generally focuses on the working spa ce and kinematics analysis, dynamics are rarely considered. To meet the requirements of the modern fast and efficient production, reduce the cost and promote the machine tool’s acceleration character, not only should we analyze the kinematics of machine tool, but also we should study its dynamics a nd optimize the structure on the basis of analysis. In this paper, the kinem atics and dynamics of a 5-DOF (degrees of freedom) machine tool with novel para llel mechanism that has three moving DOF and one rotating DOF are studied by Rob ot-Wittenberg method. The dynamics character of the parallel robotic machine is analyzed and used to guide the structure design of machine tool. At last, the c orrectness is verified through a numerical simulation of 5-DOF. Hence, the dyna mics model can generally solve the problems existing in the parallel and hybrid machine tools. The dynamics character of the parallel robotic machine is studied and analyzed in quantity. The dynamics equation of the system can be written as This is a set of differential equations of four DOF system. Theoretically, the c losed solution of the forward and inverse problems can be gained by solving the above equations. The system equations quite suit to program at the computer. Whe n the forces are given, the state variables’ numerical solution can be gain ed through integral; and when the dynamics parameters are given, the forces can also be solved. But the multiple valued phenomena can not be avoided. We have developed simulation software based on the dynamics model presented by t his paper. The different effects of the structure parameters can be given by numerical simulation.

Gait Analysis of a Radial Symmetrical Hexapod Robot Based on Parallel Mechanisms

Most gait studies of multi-legged robots in past neglected the dexterity of robot body and the relationship between stride length and body height.This paper investigates the performance of a radial symmetrical hexapod robot based on the dexterity of parallel mechanism.Assuming the constraints between the supporting feet and the ground with hinges,the supporting legs and the hexapod body are taken as a parallel mechanism,and each swing leg is regarded as a serial manipulator.The hexapod robot can be considered as a series of hybrid serial-parallel mechanisms while walking on the ground.Locomotion performance can be got by analyzing these equivalent mechanisms.The kinematics of the whole robotic system is established,and the influence of foothold position on the workspace of robot body is analyzed.A new method to calculate the stride length of multi-legged robots is proposed by analyzing the relationship between the workspaces of two adjacent equivalent parallel mechanisms in one gait cycle.Referring to service region and service sphere,weight service sphere and weight service region are put forward to evaluate the dexterity of robot body.The dexterity of single point in workspace and the dexterity distribution in vertical and horizontal projection plane are demonstrated.Simulation shows when the foothold offset goes up to 174 mm,the dexterity of robot body achieves its maximum value 0.164 4 in mixed gait.The proposed methods based on parallel mechanisms can be used to calculate the stride length and the dexterity of multi-legged robot,and provide new approach to determine the stride length,body height,footholds in gait planning of multi-legged robot.

Kinematics and Dynamics Analysis of Drive Mechanism of Parallel Four-Bar Energy-Saving Pumping Unit

The conventional beam pumping unh consumes a large amount of energy due to its unsmooth movement. In this work, we design a new energy-saving parallel four-bar pumping unit and derive the kinematic and dynamic law of the drive mechanism systematically by theoretical method. For the given target technical parameter, the theoretical results are verified by computer simulation, which shows that the simulation dynamic curves agree well with the theoretical ones and the calculated power consumption is low. Theoretical analysis shows that the newly designed pumping unit reduces average power by 28.8% compared with its conventional counterpart. The much lower theoretical energy consumption and the better dynamic performance indicate that the new energy-saving pumping unit is well designed and will have a significant application prospect.

DYNAMICS ANALYSIS OF 2-DOF SPHERICAL PARALLEL MECHANISM

The analytical formulations of the velocity and the acceleration of a 2-DOF spherical parallel mechanism are derived by the screw theory. Based on building its dynamics model by the principle of virtual work and reciprocal product of the screw, the equation of the motor moment is obtained. Through the transformation of dynamics model, the configuration space method of the dynamics equation and the corresponding coefficients are presented. Finally, the result of an example shows that the inertia moment and the gravity play a more important role than the coriolis and centrifugal moment, and the former is ten times of the latter in the magnitude. So, the latter can be neglected only when the velocity of mechanism is very slow.

A Hyper-redundant Elephant’s Trunk Robot with an Open Structure:Design,Kinematics,Control and Prototype

As for the complex operational tasks in the unstructured environment with narrow workspace and numerous obstacles,the traditional robots cannot accomplish these mentioned complex operational tasks and meet the dexterity demands.The hyper-redundant bionic robots can complete complex tasks in the unstructured environments by simulating the motion characteristics of the elephant’s trunk and octopus tentacles.Compared with traditional robots,the hyper-redundant bionic robots can accomplish complex tasks because of their flexible structure.A hyper-redundant elephant’s trunk robot(HRETR)with an open structure is developed in this paper.The content includes mechanical structure design,kinematic analysis,virtual prototype simulation,control system design,and prototype building.This design is inspired by the flexible motion of an elephant’s trunk,which is expansible and is composed of six unit modules,namely,3UPS-PS parallel in series.First,the mechanical design of the HRETR is completed according to the motion characteristics of an elephant’s trunk and based on the principle of mechanical bionic design.After that,the backbone mode method is used to establish the kinematic model of the robot.The simulation software SolidWorks and ADAMS are combined to analyze the kinematic characteristics when the trajectory of the end moving platform of the robot is assigned.With the help of ANSYS,the static stiffness of each component and the whole robot is analyzed.On this basis,the materials of the weak parts of the mechanical structure and the hardware are selected reasonably.Next,the extensible structures of software and hardware control system are constructed according to the modular and hierarchical design criteria.Finally,the prototype is built and its performance is tested.The proposed research provides a method for the design and development for the hyper-redundant bionic robot.

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.

Hardware-in-the-loop simulation for the contact dynamic process of flying objects in space

In the one-gravity environment on the ground, the simulation of the contact process of two flying objects in the zero-gravity environment of space has been a challenging issue since humans first explored space by flying objects. Hardware-in-the-loop （HIL） simulation is an important and effective method to test the usability, reliability, and safety of real docking mechanisms in space. There are four main issues for HIL simulation systems： Design of simulators capable of high frequency response, high motion precision, high velocity, and rapid acceleration; compensation for simulation distortion; design of a control model for the HIL simulation process; and experimental verification. Here, we propose a novel HIL simulator system with a 6-DOF 3-3 perpendicular parallel mechanism and a 3-DOF 3-PRS parallel mechanism; discover the principle of simulation distortion; present distortion compensation models for the force measurement system, dynamic response, and structural dynamics of the simulator; and provide a control model for the HIL simulation process. Two kinds of experiments were performed on the pas- sive-undamped elastic rod and the docking mechanisms to test their performances and to verify the effectiveness and usability of the HIL simulator. The HIL simulation system proposed in this paper is useful for developing space docking, berthing, refu- eling, repairing, upgrading, transporting, and rescuing technologies.

Dynamics of 3-DOF Hybrid Robot Manipulator

This paper introduces a 3-dof hybrid robotic manipulator which is constructed by combining a parallel mechanism and a pantograph to increase stiffness as well as workspace. And by analyzing its kinematics and dynamics with Lagrange’s method, the dynamic model is obtained which is essential for feed-forward control of the manipulator. An explicit solution is given out. Finally, a simulation test is carried out on computers.

Configuration Design and Kinematic Performance Analysis of a Novel 4-DOF Parallel Ankle Rehabilitation Mechanism with Two Virtual Motion Centers

Aiming at the problem that the existing ankle rehabilitation robot is difficult to fully fit the complex motion of human ankle joint and has poor human-machine motion compatibility,an equivalent series mechanism model that is highly matched with the actual bone structure of the human ankle joint is proposed and mapped into a parallel rehabilita-tion mechanism.The parallel rehabilitation mechanism has two virtual motion centers(VMCs),which can simulate the complex motion of the ankle joint,adapt to the individual differences of various patients,and can meet the reha-bilitation needs of both left and right feet of patients.Firstly,based on the motion properties and physiological structure of the human ankle joint,the mapping relationship between the rehabilitation mechanism and ankle joint is determined,and the series equivalent model of the ankle joint is established.According to the kinematic and con-straint properties of the ankle equivalent model,the configuration design of the parallel ankle rehabilitation robot is carried out.Secondly,according to the intersecting motion planes theory,the full-cycle mobility of the mechanism is proved,and the continuous axis of the mechanism is judged based on the constraint power and its derivative.Then,the kinematics of the parallel ankle rehabilitation robot is analyzed.Finally,based on the OpenSim biomechanical soft-ware,a human-machine coupling rehabilitation simulation model is established to evaluate the rehabilitation effect,which lays the foundation for the formulation of a rehabilitation strategy for the later prototype.

Algebraic Method‑Based Point‑to‑Point Trajectory Planning of an Under‑Constrained Cable‑Suspended Parallel Robot with Variable Angle and Height Cable Mast

To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.

Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with Kinematic Redundancy

The kinematic redundancy is considered as a way to improve the performance of the parallel mechanism.In this paper,the kinematics performance of a three degree-of-freedom parallel mechanism with kinematic redundancy(3-DOF PM-KR)and the influence of redundant parts on the PM-KR are analyzed.Firstly,the kinematics model of the PM-KR is established.The inverse solutions,the Jacobian matrix,and the workspace of the PM-KR are solved.Secondly,the influence of redundancy on the PM-KR is analyzed.Since there exists kinematic redundancy,the PM-KR possesses fault-tolerant performance.By locking one actuating joint or two actuating joints simultaneously,the fault-tolerant workspace is obtained.When the position of the redundant part is changed,the workspace and singularity will be changed.The results show that kinematic redundancy can be used to avoid singularity.Finally,the simulations are performed to prove the theoretical analysis.

香蕉采摘与吊运作业机器人运动与动力性能分析

由于香蕉果串的结果高度和果形尺寸较大,且采摘过程极易发生损伤,给其采摘带来极高难度,目前仍停留在比较落后的人工采摘方式上,劳动强度大。为此,提出了一种香蕉采摘与吊运作业机器人,可将香蕉果柄的切割、夹持和香蕉果串的吊放作业整体性完成,其机械系统主要由伺服连杆机械臂、夹持与切割末端执行器和液压履带行走动力单元等部分组成。工作时,末端执行器夹持与切割香蕉果柄的直径范围为40~150mm,液压履带车行走的最大行走速度为1.07m/s。通过基于ADAMS的机械系统运动和动力学仿真分析获得了伺服连杆机械臂的作业范围,以香蕉按照宽窄行宜机化种植模式为基础,对接近实际情况的伺服驱动作业流程进行了仿真研究,验证了各伺服电机的驱动能力。

下肢外骨骼康复机器人仿真和试验分析

目的为了帮助下肢运动障碍者进行有序康复训练,设计一种下肢外骨骼康复机器人,动力源驱动下肢交叉摆动模拟人类正常步态行走,实现双下肢协调运动,帮助下肢运动障碍者完成康复训练。方法建立外骨骼机器人三维模型、下肢外骨骼机器人D-H模型,对下肢外骨骼康复机器人进行正、逆运动学分析,并将模型导入ADAMS,创建运动副与驱动函数进行运动学仿真,在此基础上制作样机并进行动力学测试试验分析。结果正、逆运动学验证了外骨骼康复机器人空间运动的合理性,ADAMS运动仿真结果与理论计算具有良好一致性,从而保证设计的下肢外骨骼结构与穿戴者下肢同步协调。仿真分析发现理论计算和仿真的误差主要来源于驱动函数误差,动作误差最大为2.15 cm。试验验证髋关节、膝关节运动与参考输入运动具有一致性。但是运动存在误差,髋关节平均误差为5.57°,膝关节平均误差为5.45°,实验发现电机扭矩不足是引起运动误差的首要因素,其次是零件加工误差和装配误差。结论通过理论计算、仿真与试验分析验证了方案的可行性,发现驱动误差、零件加工精度和装配精度可带来误差。研究结果可为进一步完善机器人性能和研究康复机器人动力学影响因素提供基础和参数依据。

无寄生运动3-DOF 2T1R并联机构拓扑设计与分析

为充分研究少自由度并联机构所具备优势,拓宽其应用领域,设计并研究一种含冗余支链且无寄生运动三自由度两平移一转动(2T1R)并联机构,完成运动学和动力学分析。基于方位特征集(POC)的拓扑机构学理论方法,设计了一种含冗余支链且无寄生运动的两平移一转动并联机构,并进行拓扑分析,结果表明:该机构还具有部分运动解耦特性;根据基于拓扑特征运动学的建模方法,求得机构位置正反符号解;又基于位置反解分析了机构奇异性,基于位置正解给出了工作空间;基于虚功原理的序单开链法对机构进行动力学建模,求得了该机构移动副处的驱动力以及两个子运动链(SKC)连接处的支反力;概念设计了该机构的一种应用场景。

正解符号化且运动解耦的2T1R并联机构拓扑设计与分析

基于方位特征(POC)方程的并联机构设计理论与方法,设计了一种全部由低副组成、具有位置正解符号化且部分运动解耦的两平移一转动(2T1R)并联机构,并对机构的主要拓扑特征(POC、自由度、耦合度、运动解耦性)进行分析与计算;基于拓扑特征运动学建模原理,导出机构符号式位置正解和反解;同时,由位置反解分析了机构奇异性,基于符号式位置正解求解了机构工作空间;根据基于虚功原理的序单开链法,对该机构动力学性能进行分析,计算得施加在3个驱动副上的驱动力;最后,对该机构应用于无人机操作及其安全着陆的动作原理进行了概念设计阐述。