Translational Parallel Manipulator Research Articles

Tri-pyramid Robot: Design and kinematic analysis of a 3-DOF translational parallel manipulator

3-DOF translational parallel manipulators have been developed in many different forms, but they still have respective disadvantages in different applications. To overcome their disadvantages, the structure and constraint design of a 3-DOF translational parallel manipulator is presented and named the Tri-pyramid Robot. In the constraint design of the presented manipulator, a conical displacement subset is defined based on displacement group theory. A triangular pyramidal constraint is presented and applied in the constraint designs between the manipulator@?s subchains. The structural properties including the decoupled motions, overconstraint elimination, singularity free workspace, fixed actuators and isotropic configuration are analyzed and compared to existing structures. The Tri-pyramid Robot is constrained and realized by a minimal number of 1-DOF joints. The kinematic position solutions, workspace with variation of structural parameters, Jacobian matrix, isotropic and dexterity analysis are performed and evaluated in the numerical simulations.

Tri-pyramid Robot: stiffness modeling of a 3-DOF translational parallel manipulator

SUMMARYThis paper presents a 3-DOF (degree of freedom) translational parallel manipulator named the Tri-pyramid Robot. Compared to the developed 3-DOF translational parallel manipulators, the Tri-pyramid Robot is designed based on conical displacement subset to exhibit better kinematic characteristic. The inverse position solution is obtained through closed-loop constraint analysis and used to formulate the overall Jacobian matrix of constraints and actuations based on the theory of reciprocal screws. Furthermore, by considering the stiffness of all links, joints, actuators, fixed, and moving platforms, the output stiffness matrix of the Tri-pyramid Robot is derived by the transformations of loads and deformations in the closed-loop form. The relations between the virtual input-output displacements are analyzed by the overall Jacobian matrix and used to build the manipulator's stiffness model. Stiffness performance is evaluated by the extreme eigenvalues of the output stiffness matrix in the reachable workspace. By considering the variations of the structural parameters and the distribution of the output stiffness, the maximal stiffness workspace is obtained through numerical optimization, providing, thereby, basic constraints for the parametric design of the Tri-pyramid Robot.

A 2-legged XY parallel flexure motion stage with minimised parasitic rotation

XY compliant parallel manipulators (aka XY parallel flexure motion stages) have been used as diverse applications such as atomic force microscope scanners due to their proved advantages such as eliminated backlash, reduced friction, reduced number of parts and monolithic configuration. This paper presents an innovative stiffness centre based approach to design a decoupled 2-legged XY compliant parallel manipulator in order to better minimise the inherent parasitic rotation and have a more compact configuration. This innovative design approach makes all of the stiffness centres, associated with the passive prismatic (P) modules, overlap at a point that all of the applied input forces can go through. A monolithic compact and decoupled XY compliant parallel manipulator with minimised parasitic rotation is then proposed using the proposed design approach based on a 2-PP kinematically decoupled translational parallel manipulator. Its load–displacement and motion range equations are derived, and geometrical parameters are determined for a specified motion range. Finite element analysis comparisons are also implemented to verify the analytical models with analysis of the performance characteristics including primary stiffness, cross-axis coupling, parasitic rotation, input and output motion difference and actuator nonisolation effect. Compared with the existing XY compliant parallel manipulators obtained using 4-legged mirror-symmetric constraint arrangement, the proposed XY compliant parallel manipulators based on stiffness centre approach mainly benefits from fewer legs resulting in reduced size, simpler modelling as well as smaller lost motion. Compared with existing 2-legged designs with the conventional arrangement, the present design has smaller parasitic rotation, which has been proved from the finite element analysis results.

Kinematic calibration of a 2-DOF translational parallel manipulator

Two types of kinematic calibration method for a 2-DOF (degrees of freedom) translational parallel manipulator are proposed using different error models. A calibration experiment is performed on both methods using an Absolute Laser Tracker and the results are compared. Two error models of the 2-DOF translational parallel manipulator are established using differential method and linear perturbation method, respectively. The two error models are solved using both the least squares method and linear equations. The results for the two different calibration methods show that the error model based on differential method is more effective in improving the accuracy of the 2-DOF translational parallel manipulator. Overall, the absolute position error of the 2-DOF translational parallel manipulator is significantly reduced to 0.13 mm from 0.93 mm after kinematic calibration.

A new asymmetrical mass distribution method on the analysis of universal “force-sensing” model for 3-DOF translational parallel manipulator

Purpose – The characteristic of static is quite important especially for the manipulator with force feedback. This paper aims to improve the traditional static model by considering the limitations such as lacking of versatility and ignoring gravity of links. For this purpose, a new asymmetric mass distribution method on the analysis of universal “force-sensing” model has been put forward to overcome the limitations. Design/methodology/approach – Through the forces and torques analysis of every link and the moving platform, the static model of 3-RUU manipulator is acquired. Then, based on the physical meaning analysis of every part in the static model of 3-RUU manipulator, a new asymmetric mass distribution method on the analysis of universal “force-sensing” model can be obtained. Findings – The correctness of the static model of 3-RUU manipulator is verified by simulation results based on Pro/Engineer software and Adams software. Furthermore, experiment results based on a manipulator similar to the Omega.3 manipulator indicate that the universal “force-sensing” model can be applicable to the above manipulator. Originality/value – A new asymmetric mass distribution method on the analysis of universal static mathematical model has been put forward. Based on physical meaning of the above method, the “force-sensing” model can be established quickly and it owns versatility, which can be applicable to the 3-RUU manipulator, the Omega.3 parallel manipulator and other similar manipulators with force feedback. In addition, it can improve the accuracy of the “force-sensing” model to a great extent.

Contour Error of the 3-DoF Hydraulic Translational Parallel Manipulator

The paper deals with a selected problem of contour error for the desired tracking trajectory of the spatial 3-DoF hydraulic translational parallel manipulator (TPM). The prototype hydraulic TPM consists of a fixed base and a moving platform connected by the joints with three hydraulic linear axes. The closed-loop kinematic chains of the hydraulic TPM create a 3-RRPRR structure in which revolute joints R and prismatic joints P step out. The three equal integrated electro-hydraulic axes are prismatic joints P in which hydraulic cylinders are integrated with position measuring systems and proportional directional control valves.

Dynamic analysis and model-based feedforward control of a 2-DoF translational parallel manipulator driven by linear motors

Purpose – Based on the inverse kinematics and task space dynamic model, this paper aims to design a high-precision trajectory tracking controller for a 2-DoF translational parallel manipulator (TPM) driven by linear motors. Design/methodology/approach – The task space dynamic model of a 2-DoF TPM is derived using Lagrangian equation of the first type. A task space dynamic model-based feedforward controller (MFC) is designed, which is combined with a cascade PID/PI controller and velocity feedforward controller (VFC) to construct a hybrid PID/PI+VFC/MFC controller. The hybrid controller is implemented in MATLAB/dSPACE real-time control platform. Experiment results are given to validate the effectiveness and industrial applicability of the hybrid controller. Findings – The MFC can compensate for the nonlinear dynamic characteristics of a 2-DoF TPM and achieve better tracking performance than the conventional acceleration feedforward controller (AFC). Originality/value – The task space dynamic model-based hybrid PID/PI+VFC/MFC controller is proposed for a 2-DoF linear-motor-driven TPM, which reduces the tracking error by at least 15 percent compared with conventional hybrid PID/PI+VFC/AFC controller. This control scheme can be extended to high-speed and high-precision trajectory tracking control of other parallel manipulators by reprogramming the feedforward signals of traditional cascade PID/PI controller.

2자유도 평면 병진 병렬형 기구의 동역학 해석

In this paper, the dynamics of a novel 2-DOF planar Translational Parallel Manipulator (TPM) is analyzed. The suggested TPM is made up of two PPa (Prismatic-planar Parallelogram) legs. Since all the linear actuators are mounted on the base, the proposed TPM can be applied for high speed positioning applications. The Lagrangian equations of the first type is employed to derive the inverse dynamic equations. It is shown that the analytical inverse dynamics equations match very well with ADAMS simulations. These analytical inverse dynamics equations will be used for the real-time computed torque control in the further work.

Kinematic analyses of novel translational parallel manipulators

This study reports on the kinematic analyses of four translational parallel manipulators (3RPC, SPS + 2RPC, RPPR + 2RPC and RPPR + 2PPP) articulated with linear actuators. They are based on serially connected chains which are connected with cylindrical (C), prismatic (P), revolute (R), spherical (S) and universal (U) joints. Of these manipulators, the one which is a fully decoupled, fully isotropic and singularity-free translational parallel manipulator (RPPR+2PPP) offers a one-to-one correspondence between its input and output displacement. This makes its forward and inverse position analyses simpler with a set of linear equations to be solved. Although the other manipulators have coupled kinematics, they still have simpler forward kinematic equations over other well-known translational parallel manipulators reported in the literature. We also employ screw theory to undertake the velocity and acceleration analyses. The primary contribution of this manuscript is to show how the 3-RPC translational parallel manipulator can be gradually modified in order to obtain a fully isotropic, fully decoupled and singularity-free translational parallel manipulator.

Singularity-free design of the translational parallel manipulator IRSBot-2

The IRSBot-2 is a two degree-of-freedom translational parallel manipulator dedicated to fast and accurate pick-and-place operations. This paper deals with the determination of the design parameters of the manipulator for the IRSBot-2 to be free of parallel singularity. First, the robot architecture is introduced. The IRSBot-2 is composed of two identical spatial limbs, each one containing a proximal module and a distal module. Then, its actuation singularities and constraint singularities are analyzed. The latter are analyzed in its distal parameter space with a method based on the notion of discriminant varieties and cylindrical algebraic decomposition. Moreover, a deep analysis is carried out in order to determine the set of design parameters of the distal modules that prevents the IRSBot-2 from reaching any constraint singularity. To the best of our knowledge, such an analysis is performed for the first time. Finally, a design methodology is proposed to determine the set of design parameters associated with the proximal modules for the IRSBot-2 to be assembled and free of parallel singularity.

A Comparison Study of Two 3-UPU Translational Parallel Manipulators

A comparison study of two 3-UPU translational parallel manipulators (PMs) is investigated in this paper. The two 3-UPU PMs have identical pure translational degree of freedoms (DOFs) and an identical actuator arrangement, and thus have identical kinematics. But some differences between the two translational 3-UPU PMs impliedly exist. The two PMs differ in terms of singularity configuration, constrained forces/torques situations and stiffness. This paper focuses on discussing the differences between the two translational 3-UPU PMs. This study provides insights into PMs with identical kinematics.

A 2-DOF Translational Parallel Manipulator with Passive Universal Joints

In the paper, a novel 2-DOF (degree of freedom) plane translational parallel manipulator with passive universal joints and three legs is presented. Firstly, the 2-DOF translational parallel manipulator which has the spatial structure and high bearing capacity in the direction perpendicular to the kinematics plane is described. Then, the kinematics analysis of the 2-DOF parallel manipulator, which include inverse and forward solutions, are studied in detail, and the Jacobian matrix of the parallel manipulator is also derived based on it. Lastly, to improve the stability and bearing capacity further, the symmetric mechanisms with four legs and passive universal joints are constructed by adding a leg in parallel. The proposed 2-DOF parallel manipulator not only has the simple structure, but high stiffness especially in the direction perpendicular to kinematics plane for its spatial arrangment and passive universal joints.

Screw-System-Based Mobility Analysis of a Family of Fully Translational Parallel Manipulators

This paper investigates the mobility of a family of fully translational parallel manipulators based on screw system analysis by identifying the common constraint and redundant constraints, providing a case study of this approach. The paper presents the branch motion-screws for the 3-RP̲C-Y parallel manipulator, the 3-RCC-Y (or 3-RP̲RC-Y) parallel manipulator, and a newly proposed 3-RP̲C-T parallel manipulator. Then the paper determines the sets of platform constraint-screws for each of these three manipulators. The constraints exerted on the platforms of the 3-RP̲Carchitectures and the 3-RCC-Y manipulators are analyzed using the screw system approach and have been identified as couples. A similarity has been identified with the axes of couples: they are perpendicular to theRjoint axes, but in the former the axes are coplanar with the base and in the latter the axes are perpendicular to the limb. The remaining couples act about the axis that is normal to the base. The motion-screw system and constraint-screw system analysis leads to the insightful understanding of the mobility of the platform that is then obtained by determining the reciprocal screws to the platform constraint screw sets, resulting in three independent instantaneous translational degrees-of-freedom. To validate the mobility analysis of the three parallel manipulators, the paper includes motion simulations which use a commercially available kinematics software.

Cartesian Stiffness Matrix Mapping of a Translational Parallel Mechanism with Elastic Joints

This paper is devoted to calculating the Cartesian stiffness matrix of a translational parallel manipulator with elastic joints. The calculation takes into account the contribution of the Jacobian variation because of the change of manipulator configuration due to the elasticity and it covers the entire theoretical workspace of the manipulator. Three kineto-static adimensional indices are proposed to measure the response of the manipulator in terms of stiffness.

Modelling and Kinematic Analysis of a Built Up Linear Delta Robot

In this paper kinematic analysis of a 3-PUU translational parallel manipulator (TPM) is made by creating the forward and inverse Kinematic solutions. For a given position, control of the end effecter is then realized by using the calculated inverse kinematic parameters as reference values. For kinematic analysis relevant equations are derived from geometrical vector relations. For the forward and inverse kinematic solutions of the non-linear model a MATLAB based iterative algorithm is developed and the inverse kinematic solutions of limbs, are then used to control the end effecter position through screw rails which are driven by DC motors. After the general mechanical design of the manipulator all parts are drawn and modelled in SolidWorks, and a simulation of the motion in three dimensional space is made. To support the reliability of calculated parameters through inverse kinematic solutions, results are compared with the values of SolidWorks based simulation model of the manipulator. Furthermore a real position control with use of feed back encoders is applied and the evaluated results are compared with the results of a simulation model. Very similar and satisfactory results are obtained with both simulation and real application.

Design and Modeling of a Large-Range Modular XYZ Compliant Parallel Manipulator Using Identical Spatial Modules

To meet the need for large-range high-precision motion stages, a design methodology of XYZ compliant parallel manipulators (CPMs) is introduced at first. A spatial double four-beam module and a compliant P (prismatic) joint, composed of two spatial double four-beam modules, are then proposed. Starting from a 3-PPPR (R: revolute) translational parallel manipulator, a large-range modular XYZ CPM with identical spatial modules is constructed using the proposed design approach. Normalized analytical models for the large-range modular XYZ CPM are further presented. As a case study, a modular XYZ CPM with a motion range of 10 mm × 10 mm × 10 mm along the positive X-, Y-, and Z-axes is presented in detail, covering the geometrical parameter determination, performance characteristics analysis, buckling check, and actuation force check. The analytical models are compared with the finite element analysis (FEA) models. Finally, the dynamics consideration, manufacturability, and merits are discussed. It is shown that the proposed large-range modular XYZ CPM has the following main merits compared with existing designs: (1) large range of motion up to 20 mm × 20 mm × 20 mm and (2) reduced number of design parameters through the use of identical spatial modules, although the manufacturability is a challenging issue.

Dynamic Analysis and Computer Aided Control of a Tripod Parallel Manipulator

Abstract In this paper, modeling, dynamic analysis and position control of a 3-PUU translational parallel manipulator (TPM) is investigated. After the general mechanical design of the manipulator all parts are drawn and modeled in SolidWorks, and a simulation of the motion in three dimensional space is made. For dynamic analysis relevant equations are derived from geometrical relations of the model and finally the forward and inverse kinematic solutions of the non-linear model are developed by using a MATLAB iteration algorithm. Furthermore the transfer functions of the position control system with a block diagram are derived and a control simulation with use of MATLAB Simulink is made. Simulation results are compared with real time system responses and satisfactory results are obtained

Type Synthesis of Symmertrical Non-Overconstrained 3-DOF Translational Parallel Manipulators Based on Srew Theory

Based on screw theory,a systematic method is proposed to synthesis symmertrical non-overconstrained 3-DOF translational parallel manipulators(TPMs).Firstly,the configuration conditions of non-overconstrained TPMs are analysis.The generation of symmertrical non-overconstrained TPMs is reduced to design the structure of serial chains with one infinite pitch wrench,and to combine the same serial chains inparallel.Finally,making sure that, the union of the wrench for the same serial chains in each combination constitutes a three infinite pitch wrench system.we get all the 3-legged symmertrical non-overconstrained TPMs.

Multi-Objective Optimization of a 2-DoF Purely Translational Parallel Manipulator

The paper addresses the multi-objective optimization of a 2-DoF purely translational parallel manipulator. The kinematic analysis of the Proposed T2 parallel robot is introduced briefly. The objective functions are optimized simultaneously to improve Regular workspace Share (RWS) and Global Conditioning Index (GCI). A Multi-Objective Evolution Algorithm (MOEA) based on the Control Elitist Non-dominated Sorting Genetic Algorithm (controlled ENSGA-II) is used to find the Pareto front. The optimization results show that this method is efficient. The parallel manipulator prototype is also exhibited here.

Design and analysis of CICABOT: a novel translational parallel manipulator based on two 5-bar mechanisms

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.