A new method for optimum design of parallel manipulator based on kinematics and dynamics

This paper presents a new method for the optimum design of parallel manipulators by taking both the kinematics and dynamic characteristics into account. The optimum design of a 3-DOF 4-RRR planar parallel manipulator with actuation redundancy is investigated to demonstrate the method. The kinematic performance indices such as the conditioning index, the velocity index, and workspace area are analyzed. Further, the dynamic dexterity, which is used to evaluate the dynamic characteristics, is investigated. The corresponding atlases are represented graphically in the established design space. Based on these atlases, the geometrical parameters without dimension are determined. Then the optimum dimensional parameters are achieved based on the optimum non-dimensional result. By using the method proposed in this paper, the designer can obtain the optimum result with respect to both kinematic performance indices and dynamic performance indices. Since the dynamic performance is considered in the process of optimum design by using the method proposed in this paper, it is expected to realize the high dynamics of parallel manipulators.     

Auto-calibration of a redundant parallel manipulator based on the projected tracking error

Utilizing the projected tracking error of the redundant joint angles, we studied the calibration problem of the sensor zero positions of a planar 2-dof parallel manipulator in this paper. Based on the study of the relationship between the projected tracking error of the joint angles and the error of the sensor zero positions, a new error function is proposed for the calibration of the sensor zero positions of the parallel manipulator. It is proved that the error function is robust to the measurement error of the joint sensors, so accurate calibration results can be obtained by minimizing the error function even if the measurement of the joint angles is not accurate. With a simple searching strategy for the minimal value of the error function, we designed an auto-calibration procedure and verified the validity of the calibration procedure through real experiments on a real redundant planar 2-dof parallel manipulator.     

A New Parameter Design Method of a 6-DOF Parallel Motion Simulator for a Given Workspace

This paper introduces a new 9-DOF motion simulator that consists of a 3-DOF parallel manipulator and a 6-DOF parallel manipulator. For the 6-DOF manipulator, a new ‘3–3’-PSS parallel mechanism and a new parameter design method for a given workspace are presented. With the kinematic study of this parallel mechanism and the method of Lagrange multipliers, we have found several key points that represent the worst performance of the manipulator within the given workspace. When a position workspace is given, by checking the manipulator's performances at these key points, one can quickly find out whether the manipulator with certain parameters meets the requirements within this workspace. Furthermore, several figures that can find the appropriate parameters are plotted. This key point method can make the design of parameters much quicker and easier for manipulators.     

A study on the effect of structure parameters on the dynamic characteristics of a PRRRP parallel manipulator

This paper studies the effect of structure parameters on the dynamic characteristics of a planar PRRRP parallel manipulator. The stiffness model is derived by considering the effect of joint. Based on the stiffness matrix, the vibration equation of this parallel manipulator is investigated to study the dynamic characteristics. The natural frequency is computed, and the effect of Y and Z coordinate on the natural frequency is discussed. Moreover, the sensitivity model of the dynamic characteristic to critical structure parameters is proposed. The thickness of column and leg, the radial stiffness of bearing, and the lumped mass on the end-effector are determined based on the natural frequency and sensitivity index. The results are useful to the structure design of parallel manipulators.     

Design of a single motor,tendon driven redundant manipulator with reduced driving joint torques

Lightweight manipulator design is one of the diverse and rich research fields in the area of robotics. It has become increasingly important to develop manipulators with reduced cost, high energy e?ciency and with low inertia. There are numerous design concepts proposed in the past decades such as designing lightweight joints or locating the actuators at the base. Reduction of number of actuators used has added advantages such as cost reduction, reduced power consumption, compact in design apart from reduction of weight. This paper presents a lightweight tendon drive redundant manipulator design with reduced joint torque using a single motor. The proposed design has reduced the number of actuators used. Thus the design is not only effective in reducing driving joint torques but also minimizes the number of actuators required and the power consumption. Driving joint torques computed for both conventional and for the proposed manipulator design highlight the significance of the proposed manipulator.     

Comparison of 3-RPR planar parallel manipulators with?regard to their kinetostatic performance and sensitivity to geometric uncertainties

This paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators. First, the manipulators under study as well as their degeneracy conditions are presented. Then, an optimization problem is formulated in order to obtain their maximal regular dexterous workspace. Moreover, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, we compare two non-degenerate and two degenerate 3-RPR planar parallel manipulators with regard to their dexterity, workspace size and sensitivity. Finally, two actuating modes are compared with regard to their sensitivity.     

Dynamic model based nonlinear tracking control of a planar parallel manipulator

Based on the dynamic model, a novel nonlinear tracking controller is developed to overcome the nonlinear dynamics and friction of a planar parallel manipulator. The dynamic model is formulated in the active joint space, and the active joint friction is described with the Coulomb + viscous friction model. A nonlinear tracking controller is designed to eliminate the tracking error by using the power function. The nonlinear tracking controller is proven to guarantee asymptotic convergence to zero of both the tracking error and error rate with the Barbalat’s lemma. The trajectory tracking experiment of the proposed controller is implemented on an actual five-bar planar parallel manipulator both at the low-speed and high-speed motion. Moreover, the control performances of the proposed controller are compared with the results of the augmented PD (APD) controller.     

Free-floating closed-chain planar robots: Kinematics and path planning

The study of free-floating manipulators is important for the success of robotics program in space and in the design of innovative robot systems which can operate over a large workspace. In order to study the fundamental theoretical and experimental issues encountered in space robotics, a closed-chain planar manipulator was built at Ohio University (OU) which floats on a flat table using air bearings. Due to the absence of external forces in the plane of the table and couples normal to this plane, the linear momentum in the plane and the angular momentum normal to this plane are conserved. It is well known that the linear momentum equations are holonomic while the angular momentum equation is nonholonomic. Due to this nonholonomic behavior, the path-planning schemes commonly used for fixed-base manipulators do not directly apply to free-floating manipulators. In this paper, we present an algorithm for motion planning of planar free-floating manipulators based on the inverse position kinematics of the mechanism. It is demonstrated that the inverse position kinematics algorithms, commonly used for fixed-base manipulators, can be successfully applied to free-floating manipulators using an iterative search procedure to satisfy the nonholonomic angular momentum constraints. This procedure results in paths identical to those predicted by inverse rate kinematics. The inverse position kinematics algorithm is then used to avoid singularities during motion to result in successful paths. The results of the simulation of this algorithm using parameter estimates of the OU free-floating robot are presented.     

带滑移铰空间机械臂运动规划的双向逼近方法

以双向逼近方法为基础,讨论了载体姿态与位置均不受控制的带滑移铰空间机器臂的运动规划问题．该方法利用系统的非完整动力学性质,仅通过对空间机器臂关节铰运动的控制,即可达到对载体姿态及机械臂关节位置的双重控制效果,从而减少了载体姿态控制燃料的消耗,有效延长了空间机械臂系统的使用寿命．系统数值仿真证明了该方法的有效性．     

Adaptive time-varying super-twisting global SMC for projective synchronisation of flexible manipulator

In this paper, a synchronisation strategy between a controlled master and three-slave two-link flexible manipulators is proposed. Two out of the three slaves are identical with the master, whereas the third one is non-identical. The master and the slave manipulators are modelled by assumed modes and lumped parameter methods, respectively. The 12 states of the master manipulator are synchronised to the 8 states of each slave manipulator. Such projective synchronisation is also not available in the literature. A global sliding mode controller is designed first for the master manipulator to track the desired trajectory. Next, the synchronisation between the master and the slaves is achieved by designing an adaptive time-varying super-twisting global sliding mode controller. The simulation results reveal that the performances of the proposed controller in terms of (i) steady-state error of synchronisation, (ii) synchronisation time and (iii) links deflection are much better than the existing controller proposed in 2016.     

Mechatronic design,experimental setup,and control architecture design of a novel 4 DoF parallel manipulator

Although parallel manipulators started with the introduction of architectures with six degrees of freedom, a vast number of applications require less than six degrees of freedom. Consequently, scholars have proposed architectures with three and four degrees of freedom, but relatively few four degrees of freedom parallel manipulators have become prototypes, especially of the two rotation and two translation motion types. In this article, we explain the mechatronics design, prototype, and control architecture design of a four degrees of freedom parallel manipulators with two rotation and two translation motions. We chose to design a four degrees of freedom manipulator based on the motion needed to complete the tasks of lower limb rehabilitation. To the author’s best knowledge, parallel manipulators between three and six degrees of freedom for rehabilitation of lower limb have not been proposed to date. The developed architecture enhances the three minimum degrees of freedom required by adding a four degrees of freedom, which allows combinations of normal or tangential efforts in the joints, or torque acting on the knee. We put forward the inverse and forward displacement equations, describe the prototype, perform the experimental setup, and develop the hardware and control architecture. The tracking accuracy experiments from the proposed controller show that the manipulator can accomplish the required application.     

Nonlinear response of a flexible Cartesian manipulator with payload and pulsating axial force

In this present work, the nonlinear response of a single-link flexible Cartesian manipulator with payload subjected to a pulsating axial load is determined. The nonlinear temporal equation of motion is derived using D’Alembert’s principle and generalised Galerkin’s method. Due to large transverse deflection of the manipulator, the equation of motion contains cubic geometric and inertial types of nonlinearities along with linear and nonlinear parametric and forced excitation terms. Method of normal forms is used to determine the approximate solution and to study the dynamic stability and bifurcations of the system. These results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion. Influences of amplitude of the base excitation, mass ratio, and amplitude of static and dynamic axial load on the steady state responses of the system are investigated for three different resonance conditions. For some specific conditions, the results obtained in this work are found to be in good agreement with the previously published experimental work. The results obtained in this work will find applications in the design of flexible Cartesian manipulators with payload.     

An evolutionary approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. The pseudoinverse control is not repeatable, causing drift in joint space which is undesirable for physical control. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms, leading to an optimization criterion for repeatable control of redundant manipulators, and avoiding the joint angle drift problem. Computer simulations performed based on redundant and hyper-redundant planar manipulators show that, when the end-effector traces a closed path in the workspace, the robot returns to its initial configuration. The solution is repeatable for a workspace with and without obstacles in the sense that, after executing several cycles, the initial and final states of the manipulator are very close.     

Forward position analysis of 6-3 Linapod parallel manipulators

In this study closed-form solutions to the forward kinematic problems are obtained for a particular type of six degree-of-freedom parallel manipulator called 6-3 Linapod. The 6-3 Linapod parallel manipulators have a 6-3 PSS (or PUS) structure, and forward kinematic solutions are obtained by using the solution procedure for 6-3 SPS (or UPS) manipulators. In this procedure, a 6-3 Linapod is first transformed into its equivalent mechanism, namely an inclined 3RS manipulator, and then the condition that the three spherical joints on the moving platform form an equilateral triangle leads us to obtain three polynomial equations in three unknowns. These equations are solved by using Sylvester dialytic elimination method. Each set of real roots corresponds to a particular configuration of the manipulator. Solutions so obtained are verified by performing inverse position analysis. A method to identify configurations containing crossed links is presented in this study, which is based on the interpretation of link crossing as intersection of a link with a triangle, whose vertices are positions of joints on the corresponding links.     

DYNAMICS MODELING AND EXPERIMENT OF A FLEXIBLE CAPTURING MECHANISM IN A SPACE MANIPULATOR 1)

柔性捕获机构是空间机械臂的关键性部件, 对空间在轨服务过程中的抓捕操作起着至关重要的作用. 捕获机构的原理分析与仿真建模工作对在轨捕获工况预测分析和任务规划有着重要的应用价值. 本文以空间机械臂的末端柔性捕获机构为研究对象, 建立了柔性捕获机构软捕获过程的动力学仿真模型. 考虑了软捕获过程中柔性绳索的空间构型和大变形特性, 采用绝对节点坐标方法建立了三维空间柔性绳索单元, 并通过引入一圆柱参考坐标系来建立柔性绳索与目标适配器端刚性捕获杆的接触碰撞模型. 为满足三维运动工况验证, 搭建了纯被动边界条件的悬吊实验, 通过对比软捕获过程中被捕获目标的运动信息和受力信息, 验证了模型的准确性. 实验结果表明该模型能够有效地模拟在轨捕获任务中柔性机构软捕获阶段的动力学行为, 可以用于后续与空间机械臂联合仿真任务预测以及作为地面气浮台二维试验的必要补充. 此外, 针对在轨任务中的舱外状态巡检和漂浮目标捕获两种典型工况, 进行了机械臂捕获动力学联合仿真分析, 在给定条件下成功完成软捕获阶段的操作.     

Dexterity measures and their use in quantitative dexterity comparisons

The majority of proposed dexterity measures rely on the use of the condition number of the manipulator’s Jacobian matrix mapping actuator velocities to end effector velocities. Unfortunately, for the vast majority of manipulators, the conventional Jacobian matrix has inconsistent units making the aforementioned measures dependent on units and scale. Recently, a Jacobian matrix mapping the joint velocities to independent Cartesian velocity components of three points on the end effector was proposed. In most cases, this Jacobian matrix has consistent units and in many cases it is dimensionless. This dimensionally-homogeneous Jacobian matrix yields meaningful dexterity measures that allow quantitative dexterity comparisons between manipulators with different architectures. Although these new measures were originally proposed within the context of parallel manipulator design and analysis, they can also be used for serial architectures. In this paper, the analysis of the Tricept manipulator’s dexterous workspace, as a function of architectural variables, is provided through the use of a quantitative metric for dexterity. Furthermore, the generality of this metric is also demonstrated by first employing it to analyze a serial manipulator and then comparing it to a parallel manipulator having the same degrees-of-freedom. The paper also proposes a strategy to deal with singularities introduced mathematically by the novel Jacobian formulation.     

空间机械臂柔性捕获机构建模与实验研究

柔性捕获机构是空间机械臂的关键性部件, 对空间在轨服务过程中的抓捕操作起着至关重要的作用. 捕获机构的原理分析与仿真建模工作对在轨捕获工况预测分析和任务规划有着重要的应用价值. 本文以空间机械臂的末端柔性捕获机构为研究对象, 建立了柔性捕获机构软捕获过程的动力学仿真模型. 考虑了软捕获过程中柔性绳索的空间构型和大变形特性, 采用绝对节点坐标方法建立了三维空间柔性绳索单元, 并通过引入一圆柱参考坐标系来建立柔性绳索与目标适配器端刚性捕获杆的接触碰撞模型. 为满足三维运动工况验证, 搭建了纯被动边界条件的悬吊实验, 通过对比软捕获过程中被捕获目标的运动信息和受力信息, 验证了模型的准确性. 实验结果表明该模型能够有效地模拟在轨捕获任务中柔性机构软捕获阶段的动力学行为, 可以用于后续与空间机械臂联合仿真任务预测以及作为地面气浮台二维试验的必要补充. 此外, 针对在轨任务中的舱外状态巡检和漂浮目标捕获两种典型工况, 进行了机械臂捕获动力学联合仿真分析, 在给定条件下成功完成软捕获阶段的操作.      

Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor

Conveyors are important equipment in the painting shop. Conveyors with cantilever beams have low load-carrying capacity and can carry small cars. To solve this problem, this paper presents a novel conveyor that uses redundantly actuated parallel manipulators. A method is proposed to obtain the maximum dynamic load-carrying capacity of the conveyor by optimizing the internal forces of the redundantly actuated parallel manipulators. To improve the dynamic load-carrying capacity, approaches using counterweights are utilized and compared. Furthermore, the maximum dynamic load-carrying capacity of the redundant parallel manipulator is compared with that of its nonredundant counterpart.     

Dynamical couplings analysis of rigid manipulators

A method for investigation of the dynamical couplings between the manipulator links is presented in this paper. The method is based on quasi velocities introduced originally by Hurtado (2004) and on a diagonalized Poincaré form of the Hamel representation described by Sovinsky et al. (2005). Some observations and a heuristic algorithm are proposed to determine the dynamical couplings between the rigid manipulator links. The presented strategy can be used in the design phase of manipulators and it can be realized via a simulation test. It is validated here on a 3 d.o.f. spatial manipulator.     

The bouncing motion appearing in a robotic system with unilateral constraint

The hopping or bouncing motion can be observed when robotic manipulators are sliding on a rough surface. Making clear the reason of generating such phenomenon is important for the control and dynamical analysis for mechanical systems. In particular, such phenomenon may be related to the problem of Painlevé paradox. By using LCP theory, a general criterion for identifying the bouncing motion appearing in a planar multibody system subject to single unilateral constraint is established, and found its application to a two-link robotic manipulator that comes in contact with a rough constantly moving belt. The admissible set in state space that can assure the manipulator keeping contact with the rough surface is investigated, and found which is influenced by the value of the friction coefficient and the configuration of the system. Painlevé paradox can cause either multiple solutions or non-existence of solutions in calculating contact force. Developing some methods to fill in the flaw is also important for perfecting the theory of rigid-body dynamics. The properties of the tangential impact relating to the inconsistent case of Painlevé paradox have been discovered in this paper, and a jump rule for determining the post-states after the tangential impact finishes is developed. Finally, the comprehensively numerical simulation for the two-link robotic manipulator is carried out, and its dynamical behaviors such as stick-slip, the bouncing motion due to the tangential impact at contact point or the external forces, are exhibited.