6-DOF Parallel Manipulator Research Articles

Local Modal Space Control Design for a 6-DOF Parallel Manipulator

A novel design method for modal space controller with dynamic pressure feedback is proposed for hydraulically-driven Stewart platforms. By exploiting properties of the joint-space inverse mass matrix, an analytic modal matrix is derived which can be used for transforming the highly coupled multiple-input multiple-output (MIMO) dynamics into six independent single-input single-output (SISO) channels in modal space. Based on classical control method, the modal space controller with dynamic pressure feedback is implemented and used to broaden the bandwidth of each channel in modal space separately. The effectiveness of the proposed method is examined through experiment.

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.

Kinetostatics analysis of a novel 6-DOF parallel manipulator with three planar limbs and equipped with three fingers

It is significant to develop a robot hand with high rigidity by a 6-DOF parallel manipulator(PM). However, the existing 6-DOF PMs include spherical joint which has less capability of pulling force bearing, less rotation range and lower precision under alternately heavy loads. A novel 6-DOF PM with three planar limbs and equipped with three fingers is proposed and its kinematics and statics are analyzed systematically. A 3-dimension simulation mechanism of the proposed manipulator is constructed and its structure characteristics is analyzed. The kinematics formulae for solving the displacement, velocity, acceleration of the platform, the active legs and the fingers are established. The statics formulae are derived for solving the active forces of PM and the finger mechanisms. An analytic example is given for solving the kinematics and statics of proposed manipulator and the analytic solved results are verified by the simulation mechanism. It is proved from the error analysis of analytic solutions and simulation solutions that the derived analytic formulae are correct and provide the theoretical and technical foundations for its manufacturing, control and application.

Mobility analysis and kinematic synthesis of a novel 4-DoF parallel manipulator

SUMMARYThis paper proposes a novel parallel manipulator with 1 translational and 3 rotational degrees of freedom, which may be designed as the docking equipment for large-scale component assemblage in the aircraft industry. First, the mobility and kinematic analysis of the novel manipulator is performed using the screw theory and the closed-loop vector method. To evaluate the kinematic performance of the manipulator, its workspace is calculated, and the dimensional homogeneous Jacobian matrix of this manipulator is deduced. Mainly based on a nonlinear programming approach, the kinematic dimensional synthesis is performed to optimise the dimensional parameters of this novel parallel manipulator in a prescribed workspace. The results of this paper may lay a solid foundation for the prototype design and manufacture of the novel parallel manipulator.

Motion Planning of a Novel 2-DOF Parallel Manipulator Applied as Driving Simulator of the Wheel Loader

A novel parallel manipulator with 3 legs (2 actuated by linear actuators and one supporting pillar),which is applied in a wheel loader driving simulator, is proposed in this paper. The roll angle and the pitch angle of the platform are derived in closed-form of functions of the variable lengths of two actuators. The linear velocity and acceleration of the selected point and angular velocity of the moving platform are determined and compared with measurement results obtained in the respective point and in the body of the wheel loader. The differences between the desired and actual actuator displacements are used as feedback to compute how much force to send to the actuators as some function of the servo error. A numerical example with a proposed mechanism as a driving simulator is presented

Analysis of kinematics and statics for a novel 6-DoF parallel mechanism with three planar mechanism limbs

SUMMARYA novel 6-degree-of-freedom (DoF) parallel manipulator with three planar mechanism limbs is proposed and its kinematics and statics are analyzed systematically. First, the characteristics of the proposed manipulator are analyzed and the degree of freedom is calculated. Second, the formulae for solving the displacement, the velocity, and the acceleration are derived. Third, an analytic example is given for solving the kinematics and statics of this manipulator, and the analytic solved results are analyzed and verified by the simulation mechanism. Finally, a workspace is constructed and analyzed based on a comparison between the proposed manipulator and another 6-DoF parallel manipulator.

Dynamics analysis for a novel 6-DoF parallel manipulator I with three planar limbs

A novel 6-DoF parallel manipulator I with three planar limbs is proposed and its dynamics is analyzed systematically. First, its characteristics and DoF are analyzed and calculated. Second, the formulae for solving kinematics of the moving platform and the planar limbs are derived. Third, the formulae for solving the inertial wrench applied on the planar limbs and the moving platform are derived, and dynamics formula is derived for solving dynamic active forces applied onto the planar limbs. Fourth, a singularity of the proposed parallel manipulator is determined and analyzed. Fifth, an analytic example is given for solving the kinetostatics and dynamics of the proposed parallel manipulator, and the solved results are analyzed and verified by the simulation mechanism. Finally, a workspace is constructed and analyzed by comparing with an existing 6-DoF parallel manipulator.

Operating dexterity optimization and analysis of a 3-DOF parallel manipulator for a tunnel segment assembly system

This study focuses on the operating dexterity and multi-objective optimization of a 3-DOF parallel manipulator for the segment assembly system in shield tunneling machines. Operating dexterity, including kinematic and dynamic dexterity, is defined for the manipulator. This work has been done by considering motion transmissibility and acceleration. Multi-objective optimization for the parallel manipulator has been conducted by Isight software with the objective of achieving operating dexterity. Optimal performance evaluation in terms of the dexterity and isotropy of the parallel manipulator was carried out. The optimum region for the manipulator was established based on range of the performance indices of operating dexterity. The results indicate that motion transmission and acceleration performance improved after optimization. The method provides a reference for the design, performance evaluation, and control of parallel manipulators.

Analysis and optimization of the 5-RPUR parallel manipulator

Many industrial applications need less than 6 degrees of freedom (DOF) to manipulate. On one hand, the parallel manipulators (PMs) with lower DOF have some advantages such as low manufacturing and control cost. On the other hand, they have more complicated kinematics. Among PMs with lower DOF, the 5-DOF PMs have particularly many industrial applications. Within the group of 5-DOF PMs, the three translational and two rotational (3T2R) type has more industrial applications than three rotational and two translational type. In this paper, we analyze and optimize the 5-RPUR PM which is a 3T2R type. The kinematic analysis is studied using the screw theory. The boundary and volume of the workspace is obtained using a geometrical method. In addition, singularity analysis is studied. Particle swarm optimization is utilized to optimize the workspace and the accuracy simultaneously, and achieve a roughly homogeneous accuracy index over the workspace. The boundary of the optimized workspace is depicted and we show that the optimized workspace is singularity free. The accuracy index of the manipulator is calculated and depicted in several cross-sections of the workspace.

A Novel Five-Degree-of-Freedom Parallel Manipulator and Its Kinematic Optimization

Driven by requirements of five-axis numerical control (NC) machine for its executive mechanism, this paper creatively proposes a flow path to synthesize a novel class of n-degree-of-freedom (n-DoF, 4 ≤ n ≤ 6) parallel manipulators (PMs) resorting to four steps, and takes a patented 5-DoF PM, named T5, for example to demonstrate the flow path in depth. Comparing with existing five-axis executive mechanisms, this novel class of the PMs has some advantages of light end-effector, good static, dynamic performance, and so on. Upon the underlying architecture of T5, the kinematic analysis and optimal design are carried out for the first time, in which two essential procedures are involved, one is the kinematic performance index by means of the reciprocal product associated with the wrench screw and twist screw with specific physical meaning, the other is the design method adopted to perform the multi-objective dimensional synthesis using an artificial intelligence approach, that is nondominated sorting genetic algorithm II (NSGA-II). This paper is aimed at laying a solid theoretical and technical foundation for the prototype design and manufacture of T5 PM.

An experimental study on motion error of hexarot parallel manipulator

In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced and investigated. This mechanism has six rotating arms, and by rotation of arms about the base, positioning and desired movement of the mechanism is achieved. Sine parallel mechanisms have a nonlinear motion while moving from an initial position to a desired position, investigation of nonlinear error in such mechanisms is of paramount importance. In this paper, inverse and forward kinematics of the mechanism are studied. Nonlinear error of the mechanism’s motion in its workspace is extracted using mid-oscillating circle and kinematic relations as well. Moreover, effective parameters on nonlinear motion error of mechanism are determined. The results obtained by theoretical method are further verified through image processing experimental tests. It is found that the results of the theoretical analysis and experimental test are in good consistency.

Robust nonlinear control of a planar 2-DOF parallel manipulator with redundant actuation

A new robust nonlinear controller is presented and applied to a planar 2-DOF parallel manipulator with redundant actuation. The robust nonlinear controller is designed by combining the nonlinear PD (NPD) control with the robust dynamics compensation. The NPD control is used to eliminate the trajectory disturbances, unmodeled dynamics and nonlinear friction, and the robust control is used to restrain the model uncertainties of the parallel manipulator. The proposed controller is proven to guarantee the uniform ultimate boundedness of the closed-loop system by the Lyapunov theory. The trajectory tracking experiment with the robust nonlinear controller is implemented on an actual planar 2-DOF parallel manipulator with redundant actuation. The experimental results are compared with the augmented PD (APD) controller, and the proposed controller shows much better trajectory tracking accuracy.

Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system

SUMMARYParallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

Deformation analysis of a 3-DOF parallel manipulator with one or two additional branches

Redundant parallel manipulators have some advantages over the nonredundant parallel manipulators. It is important to determine how many additional branches should be introduced. This paper studies whether one or two additional branches should be added to a 3-DOF parallel manipulator by comparing the flexible deformation of a 3-DOF parallel manipulator with one additional branch and that with two additional branches. The kinematic and dynamic models of the redundant parallel manipulator are derived and the flexible deformation is investigated. The flexible deformation of the manipulators with one additional branch and two branches is simulated and compared. This paper is helpful for designers to design a redundantly actuated parallel manipulator.

Adaptive control of a 3-DOF parallel manipulator considering payload handling and relevant parameter models

Abstract Model-based control improves robot performance provided that the dynamics parameters are estimated accurately. However, some of the model parameters change with time, e.g. friction parameters and unknown payload. Particularly, off-line identification approaches omit the payload estimation (due to practical reasons). Adaptive control copes with some of these structural uncertainties. Thus, this work implements an adaptive control scheme for a 3-DOF parallel manipulator. The controller relies on a novel relevant-parameter dynamic model that permits to study the cases in where the uncertainties affect: (1) rigid body parameters, (2) friction parameters, (3) actuator dynamics, and (4) a combination of the former cases. The simulations and experiments verify the performance of the proposed controller. The control scheme is implemented on the modular programming environment Open Robot Control Software (OROCOS). Finally, an experimental setup evaluates the controller performance when the robot handles a payload.

Synthesis and Analysis of 4-DOF Parallel Manipulators of Computer Aided Geometry Approach

A novel computer aided geometry approach for type synthesis and analysis of new spatial 4-DOF parallel manipulators is put forward, and create the computer simulation mechanisms of parallel manipulators using the geometric constraints and dimension driving techniques in CAD software, Based on the computer simulation mechanisms of parallel manipulators, several new spatial 4-DOF parallel manipulators are synthesized, the kinematic characteristics of the moving platforms are analyzed by computer simulation. The results of computer simulation prove that the computer aided geometric approach for solving type synthesis and kinematic analysis is not only fairly quick and straightforward, but also has the advantages of accuracy.

Workspace-constrained optimal design of three-degrees-of-freedom parallel manipulators with minimum parasitic motions by integrating interval analysis, region mapping and differential evolution

Three-degrees-of-freedom (3-DOF) parallel manipulators have many advantages such as simple structure, fewer actuators, and lower maintenance cost. However, parasitic motions may degrade the positioning accuracy of the platforms. In order to design 3-DOF parallel manipulators which can fulfil specified workspace requirements and exhibit minimum parasitic motions, the design problem is formulated into a minimax problem with workspace constraints. Then, an interval-based method is exploited to determine the feasible solution set which is derived as a union of many scattered parameter intervals (boxes). Then, a new approach based on region mapping and a powerful optimizer (namely differential evolution) is proposed to solve the optimization problem over scattered search regions. Benchmark tests show the superiority of the proposed approach. Then, the approach and interval analysis are used to solve a real-world design problem involving a 3-DOF manipulator. Numerical results demonstrate the effectiveness and advantages of the proposed design method.

Non-singular transitions between assembly modes of 2-DOF planar parallel manipulators with a passive leg

In the field of parallel manipulators, the possibility of changing assembly mode without passing through a singular configuration is well known. This kind of transitions was studied in detail for planar 3-DOF manipulators. This paper focuses on 2-DOF parallel manipulators actuated by two RRR legs and constrained to a 2-DOF motion by a passive leg. It first shows that when the platform movement is constrained to rotations and translations along a single direction, nonsingular assembly mode transitions are possible. The direct and inverse kinematic problems of the mechanism are solved. The singularity conditions are written in explicit form and geometrically interpreted. Numerical examples of nonsingular assembly mode transitions are then given. Subsequently, the paper proves that if the platform is instead constrained to translational motions, nonsingular assembly mode transitions become impossible. Remarks on the generalization of the results to a wider class of 2-DOF planar manipulators are finally given.

Compatible reachable workspaces of symmetrical Stewart–Gough parallel manipulators

The reachable workspace of a 6-DOF parallel manipulator developed using most existing methods is not a compatible workspace, as some of its subspaces might not be reachable through a continuous motion starting from the initial assembly configuration. This paper uses simple geometric properties and some characteristics of workspace boundaries to develop a compatible reachable workspace for a symmetrical Stewart–Gough manipulator. Equations that generate the entire workspace boundary can be easily determined by solving direct kinematics at five specific points, and the compatible workspace of a symmetrical manipulator can be developed within 10min using a personal computer.

Experimental Investigation on Position Analysis of 3 – DOF Parallel Manipulators

Parallel manipulators (PMs) have been the subject of study, of much robotic research during the past three decades. A parallel manipulator (PM) is a closed loop kinematic chain mechanism, that is connected to the base via multiple independent chains. The scope of this research work is to perform the position analyses of the three degrees of freedom PMs (TRIPOD and TRI-GLIDE). The present work has been planned to model the parallel manipulators using the screw joints for very accurate positioning. Experiments were conducted for the position analysis and the angular tilt of the mobile platform along x-axis and y-axis and they were found by actuating the links of the manipulators. In order to confirm the results obtained by the experimental method, ADAMS was used for solving the kinematic problems involved. The Tri-Glide and Tripod manipulators were created in ADAMS based on the fabricated models. The models were simulated for the displacement of the nut and the angle of tilt / rotation of the mobile platform about the x and y axes. The results obtained by the three methods are discussed and analyzed. In a conventional drilling machine, drilling an angular hole requires special fixtures for each specific angle. In the present work, the parallel manipulator mechanisms have been modified to an angular drilling machine, for performing angular drilling operations.