Parallel Kinematic Manipulator Research Articles

Industrial energy efficiency potentials: an assessment of three different robot concepts

The rise in energy consumption and the associated costs instigate financial concerns among industrial energy consumers. For industrial processes addressing heating and cooling as well as material transformation, a wide range of energy efficiency measures have been developed and successfully implemented. In contrast to that, most robot-based operations such as pick-and-place motions or assembly tasks still use inefficient standard concepts causing high-energy consumption and high-energy costs. Thanks to a rather low payload-to-weight ratio of new robot designs, such as parallel kinematic or hybrid robot manipulators, a high potential for energy savings is expected. This article identifies potentials for energy saving concerning industrial consumers by assessing three different robot concepts. Based on a literature review, two existing designs for robots – the conventional serial robot and the parallel kinematic robot are analysed and compared with respect to the energy utilised during a typical item placement task. Afterwards, the concept of PARAGRIP, a hybrid of the two presented robot designs is introduced and examined based on simulation regarding its energy consumption. The final results demonstrate significantly different energy consumptions between the robot concepts, identifying potential savings of about 40% in a selected industrial application scenario.

Dimension Synthesis of a Spatial Parallel Kinematic Manipulator Based on S-shaped Test Specimen

With the development of the aerospace industry, the hybrid machine tool for machining the complicated curved surface is becoming a research hotspot. The S-shaped test specimen proposed by Chengdu Aircraft Industrial Company is an effective test method to verify the ability of machining the complicated curved surface for a machine tool. Considering the spatial parallel kinematic manipulator in a hybrid machine tool provides the complicated orientation motion and its design of structure dimension affects the accuracy of the machine tool, this paper investigates the issue about dimension synthesis of the manipulator based on S-shaped test specimen. By establishing models of the S-shaped test specimen and parallel kinematic manipulator, the motion trajectory of the parallel kinematic manipulator for machining S-shaped test specimen is obtained. According to the motion trajectory and expected performance indices, the result of dimension synthesis for the manipulator is plotted and a set of suitable dimensions is achieved. With the analysis result in this paper, it is helpful to improving the accuracy of machining the S-shaped test specimen.

Concept of Improving Positioning of Pneumatic Drive as Drive of Manipulator

The paper presents a mathematical model of pneumatic actuator based on a piston rod air double acting cylinder. The model was solved using MATLAB Simulink. The results of model simulations were compared with experimental results and the drive control system was proposed. The article also includes the concept of the control system of pneumatic drive equipped with electromagnetic brake. The application of the brake is to increase the accuracy of the positioning of the actuator piston, which in turn will enable the use of this drive in the structure of parallel kinematic manipulator. Presented research provides preliminary data for assessment of the improvement of air cylinder control.

The Analysis of Trajectory Tracking Error Caused by the Tolerance of the Design Parameters of a Parallel Kinematic Manipulator

The Analysis of Trajectory Tracking Error Caused by the Tolerance of the Design Parameters of a Parallel Kinematic Manipulator

A new revised desired compensation adaptive control for enhanced tracking: application to RA-PKMs

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On the dynamic performance of parallel kinematic manipulators with actuation and kinematic redundancies

The performance of parallel kinematic manipulators may be enhanced by the use of actuation and kinematic redundancies since they promote a significant reduction in the singularities and homogenization on the actuation forces. Considering these facts, this manuscript proposes a strategy to assess if the use of one or more actuation/kinematic redundancies can be good alternatives to improve the dynamic performance of a planar parallel kinematic manipulator. This may not be a trivial task since their dynamic performance can be highly dependent on which trajectory is performed and how the redundancy is treated. To overcome the former issue, a dynamic index depicted in the system workspace is proposed. To overcome the latter issue, different optimization strategies to treat actuation and kinematic redundancies are compared. From numerical results, one can conclude that the dynamic performance of the manipulator can only be enhanced if the redundancies are treated accordingly. Moreover, the benefits of redundancy are highly dependent on the chosen trajectory, the end effector's position and orientation.

RETRACTED: Jacobian free monotonic descent algorithm for forward kinematics of spatial parallel manipulator

In order to efficiently solve a forward kinematics of parallel manipulators for real-time applications, a Jacobian free monotonic descent algorithm is proposed in this article. The system of nonlinear equations of a specified 6-degree-of-freedom parallel manipulator is established using a geometric analysis method. The proposed Jacobian free monotonic descent algorithm is modified using a traditional Newton–Raphson method by employing a first-order Taylor series expansion to numerically approximate a Jacobian matrix. A monotonic descent factor is employed for preventing the iteration from divergence even with poor initial conditions. The proposed algorithm inherits the merits of the Newton–Raphson algorithm and overcomes its drawbacks. The Jacobian free monotonic descent algorithm is programmed in MATLAB/Simulink and then is compiled to a real-time PC system with xPC target technology for implementation. The experimental results demonstrate that the proposed Jacobian free monotonic descent algorithm is ef...

Extended Model-Based Feedforward Compensation in ℒ1 Adaptive Control for Mechanical Manipulators: Design and Experiments

This paper deals with a new control scheme for Parallel Kinematic Manipulators (PKMs) based on the L1 adaptive control theory. The original L1 adaptive controller is extended by including an adaptive loop based on the dynamics of the PKM. The additional model-based term is in charge of the compensation of the modeled nonlinear dynamics in the aim of improving the tracking performance. Moreover, the proposed controller is enhanced to reduce the internal forces, which may appear in the case of Redundantly Actuated PKMs (RA-PKMs). The generated control inputs are first regulated through a projection mechanism that reduces the antagonistic internal forces, before being applied to the manipulator. To validate the proposed controller and to show its effectiveness, real-time experiments are conducted on a new four degrees-of-freedom (4-DOFs) RA-PKM developed in our laboratory.

Trajectory planning of parallel kinematic manipulators for the maximum dynamic load-carrying capacity

The objective of this paper is to identify the trajectory that accomplishes the assigned motion with the maximum dynamic load-carrying capacity (DLCC) which is subject to constraints imposed by the kinematics and dynamics of a manipulator structure. In this study, the possible trajectories of the manipulator are modeled using a parametric path representation, the optimal trajectory is then obtained using a two-loop of optimization process, in which the inner-loop optimization process based on the Simplex-type linear programming method is used to determine the dynamic loading at each discrete point along the presumed trajectory and then to formulate the DLCC; the outer-loop optimization process based on the particle swarm optimization algorithm is to solve the controlled points by maximizing the formulated DLCC. The numerical results confirm the feasibility of the optimized trajectories and demonstrate the effectiveness of the proposed algorithm for the maximum dynamic load-carrying trajectory planning of a parallel kinematic manipulator.

Performance assessment of a trajectory‐tracking approach for a manipulator with uncertainties using inverse fuzzy arithmetic

AbstractA trajectory‐tracking approach for a parallel kinematic manipulator with flexible links is investigated with respect to its robustness to undesired initial oscillations. For this purpose, an inverse fuzzy arithmetical scheme is presented and applied, in order to estimate allowable bounds on the initial conditions such that a certain tolerance band around the desired trajectory is not violated. The uncertainty bounds on the initial conditions obtained from this identification procedure indicate the influence of the disturbances on the tracking error, and thus also the robustness and the performance of the control scheme. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analysis and Design of a Reconfigurable 3-DoF Parallel Manipulator for Multimodal Tasks

This paper presents the design of a reconfigurable 3-DoF parallel kinematics manipulator. The main feature of the device is the ability to change the mobility of its moving platform from pure translation to pure rotation. The manipulator kinematics is conceived so that, when a particular configuration of the manipulator is reached, the transition between the two working modes is possible by changing the configuration of a metamorphic universal joint, which is used to connect the legs of the manipulator with the moving platform. The mechanical design of the joint, which is in fact a lockable spherical joint, is illustrated. With the joint integrated into the robot architecture, an instantaneous overconstrained kinematics is exploited to manage the phase of reconfiguration of the whole mechatronic device. A kineto-static analysis provides information about the influence of geometric parameters on its functional design. The manipulator shows simple kinematics and statics models, as well as good kinematic and static performances. Eventually, the versatility of the manipulator is shown by proposing some advanced manufacturing applications in which it could find use.

Rigid Dynamics Solution Methodology for3-PSU Parallel Kinematic Manipulators

In the world of robotics, the parallel kinematic manipulators have proved their unique potentials like rigid structural capacities, better dynamic behaviours, and excellent spatial positional accuracy for many applications. One of the prime focus areas of the paper is to test and to establish a simplified novel approach for the Inverse Kinematics problem solution for a 3-PSU Parallel Kinematic Manipulator platform. Additionally, the methodology for simulation of Inverse Kinematics has been checked and verified. The obtained solution is further used for positional simulation of virtual prototype of 3-PSU PKM using Pro/Mechanism module. Further, these derived data is used for simulation of the Rigid Dynamics Solution for PKM (considering inertial forces acting on actuator) is also simulated in case of circular contouring.

Details on the Design of a Lockable Spherical Joint for Robotic Applications

The paper proposes the mechanical design of a lockable spherical joint, which is designed to be manually or automatically configured in different kinematic solutions. The device is conceived for being used as a conventional spherical joint or converted in a universal joint, or still downgraded to a revolute pair. Therefore different configurations can be chosen according to user needs. In particular, two of the three axes of revolution, arranged in the typical roll-pitch-roll sequence of robot spherical wrists, can be locked alternately in order to provide two differently arranged universal joints. It can be demonstrated that such behavior allows to activate different mobilities of a class of reconfigurable parallel kinematics manipulators and for this task the device has been dimensioned. The transition between such mobilities occurs exploiting the concept of over-constrained kinematics, which is realized by the lockable joint during the switching phase in order to avoid an instantaneous mobility of the robot.

A new automatic motion planning algorithm for a 4-degree-of-freedom parallel kinematic manipulator based on the centre sphere method

This study investigates a new automatic motion planning algorithm for industrial robots performing a pick-and-place task in an obstacle-free workspace. The new technique finds an optimal trajectory for a parallel kinematic manipulator. The centre sphere method and multi-objective optimisation are used to solve this problem. To obtain an optimal path, an objective function that includes a hypothetical jerk fitness value, a path length function and a virtual obstacle avoidance function is defined, and the path planning problem is solved using particle swarm optimisation. For greater efficiency, the planning problem is modified to include physical constraints on the robot. The method is tested on a 4-degree-of-freedom parallel kinematic manipulator through simulations, where the optimum virtual sphere radius is obtained. Experiments are performed with an actual parallel kinematic manipulator, and a comparison of the performance of the robot executing the same tasks with trajectories obtained using the new method and two existing methods is made. The results show the efficiency and the effectiveness of the proposed approach in determining the optimal trajectory for a 4-degree-of-freedom parallel kinematic manipulator in an obstacle-free workspace.

Estimation-based ILC applied to a parallel kinematic robot

Estimation-based iterative learning control (ILC) is applied to a parallel kinematic manipulator known as the Gantry–Tau parallel robot. The system represents a control problem where measurements of the controlled variables are not available. The main idea is to use estimates of the controlled variables in the ILC algorithm, and in the paper this approach is evaluated experimentally on the Gantry–Tau robot. The experimental results show that an ILC algorithm using estimates of the tool position gives a considerable improvement of the control performance. The tool position estimate is obtained by fusing measurements of the actuator angular positions with measurements of the tool path acceleration using a complementary filter.

Global–local population memetic algorithm for solving the forward kinematics of parallel manipulators

Memetic algorithms (MA) are evolutionary computation methods that employ local search to selected individuals of the population. This work presents global–local population MA for solving the forward kinematics of parallel manipulators. A real-coded generation algorithm with features of diversity is used in the global population and an evolutionary algorithm with parent-centric crossover operator which has local search features is used in the local population. The forward kinematics of the 3RPR and 6–6 leg manipulators are examined to test the performance of the proposed method. The results show that the proposed method improves the performance of the real-coded genetic algorithm and can obtain high-quality solutions similar to the previous methods for the 6–6 leg manipulator. The accuracy of the solutions and the optimisation time achieved by the methods in this work motivates for real-time implementation of the 3RPR parallel manipulator.

An Innovative Motion Planning for 4-DOF PKM

This paper presents an innovative motion planning algorithm for pick and place operations in the industry. The new technique is to seek optimal dynamics pattern for PKM(parallel kinematic manipulator), this is achieved by two parts: First, to achieve optimal path planning, a center sphere method based on virtual obstacle path planning method is proposed to solve such path planning with Particle Swarm Optimization (PSO); Second, to enhance the efficiency of the robot, time optimal trajectory planning is finished with respect to robotic physical constraints. Then, the method applied to a 4-DOF PKM is tested by numerical simulations, some examples are presented making comparisons on same tasks assigned by different sphere radius, the simulation results show the efficiency and the effectiveness of the proposed approach to determine the optimal motion pattern for 4-DOF PKM in obstacle-free workspace.

Semi-Analytical Approach for Stiffness Estimation of 3-DOF PKM

Due to their advantageous of high stiffness, high speed, large load carrying capacity and complicated surface processing ability, PKMs (Parallel Kinematic Manipulators) have been applied to machine tools. This paper mainly addresses the issue of stiffness formulation of a three-prismatic- revolute-spherical PKM (3-PRS PKM). The manipulators consist of three kinematic limbs of identical topology structure, and each limb is composed of an actuated prismatic-revolute-spherical. In order to build up the stiffness model, kinematics, Jacobian and finite element analysis are also performed as the basis. Main works in this paper can be outlined as follows. By use of approaches of vector, inverse position analysis of 3-PRS PKM is conducted. When the independent position and orientation parameters of the end-effectors are provided, the translational distances of active prismatic joints can be determined. Then with the aid of the wrench and reciprocal screw theory, the overall Jacobian of this manipulator is formulated quickly, and which is a six by six dimensional matrix and can reflect all information about actuation and constraint singularity. After for- mulating the position analysis and Jacobian matrix, the next step is stiffness analysis. Analytical stiffness model, a function of Jacobian matrix and components stiffness matrix, is obtained first using the principle of virtual work. Stiffness model is also a six by six dimensional matrix and can provide the information of actuation and constraint stiffness simultaneously. For the complex geometry shape of some components, it is impossible to know their stiffness distributions with the varying configuration. Therefore, ANSYS technology has to be applied to compute the stiffness coefficients of these components at different configurations. Then, the computed data are used to obtain the stiffness distribution by use of the numerical fitting method. Up to now, the semi-ana- lytical stiffness model of the manipulator is completely formulated and can be applied to estimate the system stiffness of 3-PRS PKM. The model enables the stiffness of a 3-PRS PKM to be quickly estimated. Provided with the geometry parameters and load situation on tool tip, the stiffness of 3-PRS PKM system is estimated based on the stiffness matrix about tool tip which is obtained by transforming the point from the center of circle composed of three S joints to the tool tip. Then, the stiffness of system along x, y and z directions can be solved. In order to testify the correctness, the corresponding stiffness is also obtained by use of FEA software. The stress distribution and fre- quency of system are also gained by solving the FEA model.

An Efficient Method for Solving the Direct Kinematics of Parallel Manipulators Following a Trajectory

This paper presents an efficient method for solving the direct kinematics of parallel manipulators that follow a defined singularity-free trajectory. Despite the main problem is to solve the inverse kinematics, calculating the errors between the desired path and the actual path requires solving the forward kinematics which is a challenging problem. The proposed method combines closed-loop Jacobian algorithm with Newton-Raphson method to efficiently identify the desired solution. Inverse kinematics is solved using the Jacobian algorithm whereas forward kinematics is solved using Newton-Raphson method. To avoid the numerical instabilities of the Newton-Raphson method, the current state of the manipulator is used as the initial guess for the next state. This makes the numerical solution converges to the correct and desired solution quickly with a few number of iterations. The proposed method is applied to a 3RRR planar parallel manipulator and the simulation results show the effectiveness of the method. The algorithms presented in this article can be applied to other parallel manipulators. 

Configuration-dependent modal analysis of a Cartesian parallel kinematics manipulator: numerical modeling and experimental validation

In the design optimization of a robot the configuration-dependent modal analysis can be a powerful tool to be exploited when high stiffness and high dynamic performances are concurrently required. In this paper the elastodynamics of a lower-mobility Parallel Kinematic Machine for pure translational motions is analyzed. The vibrational modes and the natural frequencies of the robot are evaluated as functions of the end effector position inside the workspace. A finite element model including kinematic joints is used to perform a series of modal analyses in a grid of points inside the workspace. A polynomial regression gives continuous volume maps of the natural frequencies distributions. The numerical model is validated by comparison with experiments: a modal analysis is conducted on a set of inertance Frequency Response Functions acquired on several points of the machine components as a result of an excitation given by an instrumented hammer. A Natural Frequency Difference analysis validates the model under certain conditions and highlights some critical issues to be focused on in future works.