3-RPS Parallel Manipulator Research Articles

Multi-objective optimization design of parallel manipulators using a neural network and principal component analysis

Abstract. In this work, a multi-objective optimization design method is proposed based on principal component analysis (PCA) and a neural network to obtain a mechanism's optimal comprehensive performance. First, multi-objective optimization mathematical modeling, including design parameters, objective functions, and constraint functions, is established. Second, the sample data are obtained through the design of the experiment (DOE) and are then standardized to eliminate the adverse effects of a non-uniform dimension of objective functions. Third, the first k principal components are established for p performance indices (k<p) using the variance-based PCA method, and then the factor analysis method is employed to define its physical meaning. Fourth, the overall comprehensive performance evaluation index is established by objectively determining weight factors. Finally, the computational cost of the modeling is improved by combining the neural network and a particle swarm optimization (PSO) algorithm. Dimensional synthesis of a Sprint (3RPS) parallel manipulator (PM) is taken as a case study to implement the proposed method, and the optimization results are verified by a comprehensive performance comparison of robots before and after optimization.

Design, modeling and solar tracking control for a novel parabolic dish solar concentrator

AbstractA novel parabolic dish solar concentrator based on the improved 3-RPS parallel manipulator to drive the reflective mirror facet is proposed and designed, which can not only automatically adjust the position and orientation of the reflective mirror facet but also have the advantages of independent drive, high stiffness and no cumulative error. Then, using the coordinate transformation matrixes of the novel parabolic dish solar tracking platform, the kinematics models of the 3-RPS parallel manipulators associated with the solar altitude and azimuth angles are established. The altitude and azimuth angles of the solar movement at the installation location are calculated according to the calculation formula of solar position. To solve the problem of too many telescopic rods of the 3-RPS parallel manipulator, a genetic algorithm is used to optimize the height of the concentrator’s center of mass. Then the ideal trajectory and attitude of each telescopic rod of the 3-RPS parallel manipulators at different times of the day can be obtained with the inverse kinematics. The particle swarm optimization (PSO)-proportional-integral-derivative (PID) controller, which uses PSO algorithm to tune PID parameters, is proposed for solar trajectory tracking of the novel parabolic dish solar concentrator. The visual simulation model of the parabolic dish system is established in Simscape Multibody, and the trajectory tracking control experiment is carried out. The experimental results show that the trajectory tracking error of the novel dish solar tracking platform can be within 2.6 mm by using the PSO-PID controller.

Natural frequency prediction of the 3-RPS parallel manipulator using the substructure synthesis technology

AbstractThis paper proposed an elastodynamic modeling method combined with independent displacement coordinates and substructure synthesis technology. Firstly, the connecting rod was discretized, and the elastodynamic control equation for each element was established. The multipoint constraint element theory, linear algebra, and singularity analysis were used to identify the globally independent displacement coordinates of the manipulator. On this basis, the elastodynamic model using the substructure synthesis for the 3-PRS parallel manipulator (PM) was developed, with its natural frequencies distribution in the regular workspace discussed. The comparison with the finite-element results showed that the maximum error of the first three-order natural frequencies was within 1.03%, which verified the correctness of the analytical model. The proposed elastodynamic model included all the kinematic constraints of the manipulator without increasing the Lagrangian multiplier. The method is computationally efficient and assesses the dynamic behaviors of the mechanism at the predesign phase.

Developing of a wearable ankle rehabilitation robotic device

People with walking disorders caused by accidents or stroke can undergo treatment to restore their mobility. Traditional therapy is time-consuming and time-consuming. Therefore, a new trend was born – to facilitate rehabilitation and reduce the patient’s time. Rehabilitation robotics is an area that is constantly evolving, and new mechanisms have recently been developed to help people regain their mobility. This paper presents a 3-RPS parallel manipulator for the restoration of the ankle joint with three degrees of freedom. Parallel manipulator 3-RPS with three degrees of freedom, which was introduced by K. Hunt in 1983 as one of the sedentary parallel manipulators. Since then, 3-RPS has attracted a lot of attention from robotics and biomedical engineering engineers.

Investigation of an Underwater Vectored Thruster Based on 3RPS Parallel Manipulator

Autonomous underwater vehicles (AUVs) are important and useful tool platforms in exploring and utilizing ocean resource. However, the effect of control surfaces would decrease even invalid complete in this condition, and it is very hard for conventional AUVs to perform detailed missions at a low forward speed. Therefore, solving this problem of AUVs becomes particularly important to increase the application scope of AUVs. In this paper, we present a design scheme for the vectored thruster AUV based on 3RPS parallel manipulator, which is a kind of parallel manipulator and has advantages of compact structure and reliable performance. To study the performance and characteristics of the proposed thrust-vectoring mechanism, a series of works about corresponding kinematic and dynamic analysis have been performed through the theoretical analysis and numerical simulation. In the part of kinematics, the inverse, forward kinematics, and workspace analysis of the thrust-vectoring mechanism is presented, and the numerical simulations are accomplished to prove the feasibility and effectiveness of this design in AUVs. In order to further verify feasibility of the thrust-vectoring mechanism, based on the considerations of various affecting factors, a dynamic model of the designed thrust-vectoring mechanism is established according to theoretical analysis, and the driving forces of the linear actuator are presented through a series of numerical simulations. In addition, a control scheme based on PID algorithm is proposed for the designed vectored thruster with considering various affecting factors and the application environment. Meanwhile, the control scheme is also established and verified in MATLAB Simscape Mutibody. A series of numerical simulations of the thrust-vectoring mechanism prove the feasibility of the vectored thruster. According to equipping the designed vectored thruster, the AUVs can overcome the limit of weakening the control ability at zero or low forward speeds, and this improvement also expands the application of it, which has been scaled greatly.

A Forward, Inverse Kinematics and Workspace Analysis of 3RPS and 3RPS-R Parallel Manipulators

Parallel mechanisms are finding wide applications in manufacturing. The design methodology of parallel mechanisms is generally considered as a complex procedure. Many times they are custom designed to suit a specific task. In this work, a generalized analytical approach to forward, inverse kinematics and workspace analysis of three-degrees-of-freedom 3RPS (revolute–prismatic–spherical) and 3RPS-R (revolute–prismatic–spherical–revolute) parallel manipulator is presented. Methodology for obtaining various position and orientation of the moving platform for the provided actuation by varying the distance between the base platform and the moving platform has been discussed in detail. The actuation is given to the prismatic joint of the manipulator, which results in a variation of limb lengths, thereby altering the position and orientation of the moving platform. Sylvester dialytic elimination method is used to solve the nonlinear polynomial expressions originally obtained from the loop–closure equations. Various numerical solutions have been obtained for a different combination of limb lengths and by changing the height of the manipulator. The workspace obtained is not evenly distributed, and hence, an additional degree of freedom (DOF) of base rotation has been suggested. With the addition of one DOF, the volume of workspace obtained is enhanced without any discontinuities which would enable the manipulator to generate circular trajectories. The methodology presented in this work is general and will be suitable for similar geometries by altering the loop closure equations suitably.

Analysis of a three-extensible-rod tracker based on 3-RPS parallel manipulator for space large deployable paraboloid structure with power and communication integration

The combination of a solar array and a communication antenna can reduce the entire mass, physical size, and cost in space applications. Currently, related studies mainly focus on the combination of the two structures on one flat plate structure (FPS). Compared with the FPS, a paraboloid structure has lower surface density and higher conversion efficiency. Therefore, the novel design of a space large deployable paraboloid structure with power and communication integration (SSPCI) is proposed for spacecraft on a sun synchronous earth orbit. A novel three-extensible-rod (TER) tracker is studied in detail for the SSPCI to track the sun for power in the sunshine region or turn to face the ground station for communication in the earth's shadow region. The proposed TER tracker includes three extensible rods, where one end of each rod is connected to the base platform by a rotary joint, and the other end is connected to the mobile platform by a smart compound joint as a substitute for a spherical joint; this is known in the literature as a 3-RPS parallel mechanism. In contrast to existing serial mechanisms, it provides a simple and lightweight structure, high structural stiffness, low inertia, and more accurate positioning and pointing of the mobile platform. Meanwhile, the linear extensible rods used in the TER tracker help to reduce energy consumption, and do not require the use of large and heavy speed reducers. A kinematic model of the TER tracker is also established. Based on this kinematic model, a dynamic model is then derived by using Newton–Euler formulation. The motion trajectory of the TER tracker is planned for the SSPCI to track the sun or turn to face the ground station. By setting related parameters, the workspace and pointing accuracy of the TER tracker are analyzed and found to be satisfactory for the SSPCI, and the motion process of tracking the sun or turning to face the ground station is simulated to test the theoretical analysis. The driving force and consumed energy of the TER tracker are obtained; the results shows that the TER tracker is able to drive the SSPCI to track the sun or turn to face the ground station with the aforementioned advantages and small energy consumption. By using finite element analysis, the SSPCI supported by the TER tracker is found to have satisfactory structural performance at different orientations in a zero gravity state. Meanwhile, the TER tracker has a satisfactory operation life and can adapt well to the space thermal environment. Finally, preliminary sun tracking experiments on the TER tracker are performed on the ground successfully, indirectly proving its feasibility of the TER tracker from the mechanism principle and control mode in space applications.

Transmission index of a class of parallel manipulators with 3-RS(SR) primary structures based on pressure angle and equivalent mechanism with 2-SS chains replacing RS chain

In this paper, we present a new transmission index (TI) for kinematic performance evaluation of a class of parallel manipulators with a 3-RS (or 3-SR) structure; termed the primary structure obtained by locking all actuated joints in the manipulators. TI is based on the pressure angle that is defined in a kinematically equivalent structure, a 6-SS structure by replacing an RS chain of the primary structure with a pair of SS chains, which can reflect the practical force transmission and constraint characteristics of R joint composed of two bearings in the original manipulator. The effectiveness of TI is verified by considering 3-PRS and 3-RPS parallel manipulators. The singularity analysis, relationships between the maximum joint forces and index values, distribution of TI inside the workspace, and an application of TI to a kinematic design are demonstrated. The proposed approach can indicate both output and constraint singularity conditions with a single index, can be achieved by simple calculation process without complicated normalization, and can include the width of the revolute joint in the kinematic performance evaluation of this class of parallel manipulators.

A novel ankle rehabilitation device based on a reconfigurable 3-RPS parallel manipulator

This paper deals with the constraint-based design, optimum design and reconfiguration strategy of a 3-RPS parallel manipulator. Some design conditions related to the base and moving-platform design parameters and the three degree-of-freedom operation modes are derived. A 3-RPS parallel manipulator with two types of operation modes is generated by following those conditions. Due to its potential advantages, this manipulator is used as an ankle rehabilitation device which can cover the ankle joint motion. To derive the optimum parameters, kinematic optimization is conducted by initially parametrizing the orientation workspace and it turns out that its orientation workspace is not symmetrical. The singularity loci are traced in its orientation workspace. A performance index, named Maximum Inscribed Circle Diameter (MICD) is presented to assess the maximum tilt of the moving-platform for any azimuth angle. The distributions of MICD are plotted in the design space for different moving-platform heights. The optimum region with regard to MICD is obtained. It is noteworthy that the evolution of MICD as a function of moving-platform height in both operation modes is the opposite. Therefore, a reconfiguration strategy is proposed to ensure the moving-platform working above the minimum required orientation for any moving-platform height.

A novel vectored thruster based on 3-RPS parallel manipulator for autonomous underwater vehicles

Autonomous underwater vehicles (AUVs), which serve as main tool platforms, have played an important role in underwater surveys in scientific, military, and commercial applications. However, conventional AUVs are unable to perform missions at zero or low forward speeds because the control surfaces are ineffective in this regime.This paper presents novel vectored-thruster AUVs based on a 3-RPS parallel manipulator; the performance of the AUVs at zero and low forward speeds is found to be effectively improved. The 3-RPS parallel manipulator used for the thrust-vectoring mechanism provides certain advantages, including high positioning accuracy, fast response and compact structure. Additionally, studies of the kinematics and dynamics of the thrust-vectoring mechanism have been performed through a theoretical analysis and numerical simulation. Meanwhile, a simplified kinematics method for the 3-RPS parallel manipulator is presented and verified in MATLAB. The analysis and numerical simulation of the thrust-vectoring mechanism prove the feasibility of the design. Using this novel thrust-vectoring mechanism based on the 3-RPS parallel manipulator, the AUVs obtain the ability to provide the motion required for thrust-vectoring propulsion effectively and efficiently.

Hybrid Harvester 3-RPS Robotic Parallel Manipulator

This article presents the robotic structure and analysis of a hybrid energy harvester designed in the form of a reconfigurable 3-RPS parallel manipulator, which tracks and collects solar energy as a main function and also harvests energy from wind loads on the large solar panel. The reconfigurable design allows the harvester to lie flat on floor when destructive storms occur and then return to a working configuration after the storms. The workspace of the manipulator is determined by a minimum platform height algorithm that is developed to find all reachable positions that compose the workspace and also bring bending at root to least. The stiffness mapping of the harvester is significant in evaluating its capacity to take wind loads, which a transformation matrix is developed to convert to polar horizontal stiffness at end effector that is crucial to the intelligent control strategy in decision to enter lie-flat configuration.

Fast forward kinematics algorithm for real-time and high-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.

Operation mode analysis of 3-RPS parallel manipulators based on their design parameters

It is known that a 3-RPS parallel manipulator with an equilateral triangle base and an equilateral triangle platform has two operation modes (Schadlbauer et al., 2014) whereas a 3-RPS cube manipulator with a cube shaped base and an equilateral triangle platform has only one operation mode (Nurahmi et al., 2014). This behavior is indeed a result of the difference in the architectures of these manipulators. Therefore, this paper deals with the operation mode analysis of 3-RPS parallel manipulators based on their design parameters. Study's kinematic mapping is exploited to derive the constraint equations of the manipulators under study. A linear combination of the constraint equations independent of the joint variables is compared with a general quadric in the 7-dimensional projective space P7 to obtain some relations between the design parameters of 3-RPS manipulators with coplanar revolute joints, such that those manipulators have two operation modes. Some special cases and a numerical example are considered to emphasize the proposed approach and highlight the contributions of the paper.

High pressure waterjet propulsion with thrust vector control system applied on underwater vehicles

Maneuverability is one of the most important performances of underwater vehicles. To improve the maneuverability of underwater vehicles, a high-pressure waterjet propulsion system combined with a Thrust Vector Control System (TVCS) was presented, which controlled the sailing trajectory through adjusting the waterjet deflection angle and thrust vector instead of rudders and sterns. The TVCS was established in the form of 3RPS Parallel Manipulator and the position feedback was provided by measuring the displacements of three actuator cylinders. The relationship between the thrust direction and the displacements of the actuator cylinders was established through the procedure of solving an inverse kinematics problem. Simultaneously, the motion transformation function of the system was derived, and the Fuzzy-PID strategy was adopted. Accordingly, the Simulink model was built, and the simulation indicated that the system had good performance. In addition, the sailing trajectory was obtained, and the results showed that the turning diameter was 78 m, and it was independent of thrust and sailing speed. The underwater vehicle utilizing high-pressure water jet propulsion with TVCS had good maneuverability at either high or low speed conditions.

A Hybrid Strategy of Differential Evolution and Modified Particle Swarm Optimization for Numerical Solution of a Parallel Manipulator

This paper presents a hybrid strategy combined with a differential evolution (DE) algorithm and a modified particle swarm optimization (PSO), denominated as DEMPSO, to solve the nonlinear model of the forward kinematics. The proposed DEMPSO takes the best advantage of the convergence rate of MPSO and the global optimization of DE. A comparison study between the DEMPSO and the other optimization algorithms such as the DE algorithm, PSO algorithm, and MPSO algorithm is performed to obtain the numerical solution of the forward kinematics of a 3-RPS parallel manipulator. The forward kinematic model of the 3-RPS parallel manipulator has been developed and it is essentially a nonlinear algebraic equation which is dependent on the structure of the mechanism. A constraint equation based on the assembly relationship is utilized to express the position and orientation of the manipulator. Five configurations with different positions and orientations are used as an example to illustrate the effectiveness of the proposed DEMPSO for solving the kinematic problem of parallel manipulators. And the comparison study results of DEMPSO and the other optimization algorithms also show that DEMPSO can provide a better performance regarding the convergence rate and global searching properties.

Influence of design parameters on the singularities and workspace of a 3-RPS parallel robot

This paper presents variations in the workspace, singularities, and joint space with respect to design parameter k, which is the ratio of the dimensions of the mobile platform to the dimensions of the base of a 3-RPS parallel manipulator. The influence of the design parameters on parasitic motion, which is important when selecting a manipulator for a desired task, is also studied. The cylindrical algebraic decomposition method and Gröbner-based computations are used to model the workspace and joint space with parallel singularities in 2R1T (two rotational and one translational) and 3T (three translational) projection spaces, where the orientation of the mobile platform is represented using quaternions. These computations are useful in selecting the optimum value for the design parameter k such that the parasitic motions can be limited to specific values. Three designs of the 3-RPS parallel robot, based on different values of k, are analyzed.

Dynamics and control of variable geometry truss manipulator

Variable geometry truss manipulator (VGTM) has potential to work in the future space applications, of which a dynamic model is important to dynamic analysis and control of the system. In this paper, an approach is presented to model the dynamic equations of a VGTM by independent variables, which consists of two double-octahedral truss units and a 3-revolute-prismatic-spherical (3-RPS) parallel manipulator. In this approach, the kinematic recursive relations of two adjacent bodies and geometric constrains are used to deduce the kinematic equations of the VGTM, and Jourdain’s velocity variation principle is adopted to establish the dynamic equations of the system. The validity of the proposed dynamic model is verified by comparison of numerical simulations with the software ADAMS. Besides, an active controller for trajectory tracking of the system is designed by the computed torque method. The effectiveness of the controller is numerically proved.

Dimensionally Homogeneous Jacobian and Condition Number

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

Singularity analysis of a 3-RPS parallel manipulator using geometric algebra

Singular configurations must be avoided in path planning and control of a parallel manipulator. However, most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms. Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator. Twist and wrench in screw theory are represented in geometric algebra. Linear dependency of twists and wrenches are described by outer product in geometric algebra. Reciprocity between twists and constraint wrenches are reflected by duality. To compute the positions of the three spherical joints of the 3-RPS parallel manipulator, Tilt-and-Torsion angles are used to describe the orientation of the moving platform. The outer product of twists and constraint wrenches is used as an index for closeness to singularity(ICS) of the 3-RPS parallel manipulator. An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed, which is helpful to design, trajectory planning and control of this kind of parallel manipulator.