3-DOF Translational Parallel Manipulator Research Articles

Precision comparison of two 3-DoF translational parallel manipulators based on the orientation errors due to joint clearances

AbstractThis paper presents a comparative study of two translational parallel manipulators (TPMs) with three Degrees of Freedom (3-DOF) based on the orientation errors due to joint clearances. In fact, the kinematic and static models of the manipulators have been used to determine the analytical model of the orientation errors. Then, the maximum and the sensitivity of the orientation errors have been considered as criteria to compare the precision of the DELTA and the RAF manipulators. The maximum orientation error is determined by solving an optimization problem of the previous analytical model. The sensitivity of the orientation errors is divided into two types: one related to the sensitivity of the orientation errors to the geometric parameters and another one related to the sensitivity of the orientation error to the joint clearances. The results show that the RAF robot precision is more sensitive to the joint clearances than the DELTA one. However, this advantage of the DELTA is limited to a portion of the workspace, which is free from singular configurations.

A novel partially-decoupled translational parallel manipulator with symbolic kinematics, singularity identification and workspace determination

This paper presents a novel three-degree-of-freedom (3-DOF) translational parallel manipulator (TPM) by using a topological design method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations. The proposed PM is only composed of lower-mobility joints and actuated prismatic joints, together with the investigations on three kinematic issues of importance. The first aspect pertains to geometric modeling of the TPM in connection with its topological characteristics, such as the POC, degree of freedom and coupling degree, from which its symbolic direct kinematic solutions are readily obtained. Moreover, the decoupled properties of input-output motions are directly evaluated without Jacobian analysis. Sequentially, based upon the inverse kinematics, the singular configurations of the TPM are identified, wherein the singular surfaces are visualized by means of a Gröbner based elimination operation. Finally, the workspace of the TPM is evaluated with a geometric approach. This 3-DOF TPM features less joints and links compared with the well-known Delta robot, which reduces the structural complexity. Its symbolic direct kinematics and partially-decoupled property will ease path planning and dynamic analysis. The TPM can be used for manufacturing large work pieces.

Control of integrated electro-hydraulic servo-drives in a translational parallel manipulator

This paper deals with the kinematics, dynamics and control of an innovative application of a three degrees of freedom (3-DoF) translational parallel manipulator (TPM) with three independently controlled integrated electro-hydraulic servo-drives (IEHSDs) for the handling of heavy forgings during precision machining. With high payload of the TPM moving platform, IEHSD force and position control was analyzed using adaptive controllers. The main contribution of this study is the IEHSD control architecture, which enables highly accurate synchronization of their position confirmed experimentally during TPM trajectory tracking control. For this purpose, a synchronization controller of three IEHSDs utilizing cross-coupled control (CCC) was proposed. The synchronizing controller ensures precise control of the TPM under conditions of variable heavy technological load.

Kinematic and dynamic analysis of the Gantry-Tau, a 3-DoF translational parallel manipulator

• A closed-from mathematical model for dynamics of the Gantry-Tau is derived. • Kinematics of the Gantry-Tau is formulated and singular conditions are discussed. • Simulation studies are carried out to assess the performance of the proposed models. This paper deals with the mathematical modeling of kinematics and dynamics of the 3-degrees-of-freedom Gantry-Tau manipulator. Compared to many other parallel robots, Gantry-Tau offers a large accessible workspace and high stiffness. The kinematics of Gantry-Tau is presented which includes inverse kinematics formulation for the position, velocity and acceleration of the mechanism. Also, based on the obtained Jacobin matrices, singular configurations of the robot are studied. Afterwards, the equations of the inverse dynamic model of the Gantry-Tau are obtained through two different methods, i.e., virtual work and Newton–Euler. Finally, a case study is performed to verify the correctness of the derived models and investigate their computational efficiency.

Topology search of 3-DOF translational parallel manipulators with three identical limbs for leg mechanisms

Three-degree of freedom(3-DOF) translational parallel manipulators(TPMs) have been widely studied both in industry and academia in the past decades. However, most architectures of 3-DOF TPMs are created mainly on designers’ intuition, empirical knowledge, or associative reasoning and the topology synthesis researches of 3-DOF TPMs are still limited. In order to find out the atlas of designs for 3-DOF TPMs, a topology search is presented for enumeration of 3-DOF TPMs whose limbs can be modeled as 5-DOF serial chains. The proposed topology search of 3-DOF TPMs is aimed to overcome the sensitivities of the design solution of a 3-DOF TPM for a LARM leg mechanism in a biped robot. The topology search, which is based on the concept of generation and specialization in graph theory, is reported as a step-by-step procedure with desired specifications, principle and rules of generalization, design requirements and constraints, and algorithm of number synthesis. In order to obtain new feasible designs for a chosen example and to limit the search domain under general considerations, one topological generalized kinematic chain is chosen to be specialized. An atlas of new feasible designs is obtained and analyzed for a specific solution as leg mechanisms. The proposed methodology provides a topology search for 3-DOF TPMs for leg mechanisms, but it can be also expanded for other applications and tasks.

Triflex: variable-configuration parallel manipulators with self-aligning

This paper presents a new class of parallel manipulators called variable-configuration parallel manipulators with self-aligning. These parallel manipulators can change their form to carry out different tasks in different places, this change being managed by additional degrees-of-freedom of self-aligning. These degrees-of-freedom of self-aligning do not interfere in the motion of the moving platform, they are passive/null degrees-of-freedom that only permit changes in the form of the parallel manipulator. As an example, we present a new 3-DOF translational variable-configuration parallel manipulator with self-aligning. We develop the mobility analysis, the workspace volume analysis, the position analysis and the velocity analysis of this new 3-DOF parallel manipulator.

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.

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.

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.

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.

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.

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.

On some applications of primitive Schönflies-motion generators

In this paper, we focus on some examples of practical applications of the primitive Schonflies-motion generators that are named also the primitive X-motion generators for conciseness. We address especially the serial SCARA-type robots and the 3-dof translational parallel manipulators. Based on the limb architectures of primitive X-motion generators, we systematically introduce general architectures of serial or parallel manipulators for the purpose of practical applications. The brief account of various achievements of some of the X-motion generators that are already described in the recent literature is also proposed and their obviously singular postures are preliminarily obtained.

Analysis and mapping of the orientation error of a 3-DOF translational parallel manipulator

SUMMARYThis paper deals with the computation of the orientation error and the kinematic model of a 3-DOF translational parallel manipulator called the RAF robot. We derived a simple analytical model allowing the computation of the orientation, generated by the deformation of the PKLs, when an external load is applied to the platform. These models allowed us to map the orientation error on the workspace of the robot. We showed in particular that the minimum orientation error can be obtained when the platform is in a certain region of its workspace. Due to its analytical nature, the developed model can also be used for a sensitivity analysis in order to maximize the manipulator precision.

Dynamic modeling and control of a 3-DOF Cartesian parallel manipulator

Dynamic modeling is the basic element for controller design of mechanisms. In this paper, an effective dynamic equation of a 3-DOF translational parallel manipulator for control purpose has been derived by the Lagrange-D’Alembert formulation. The structural properties of the derived dynamic equation were proved so that the vast control strategies developed for the serial counterparts can be easily extended for controlling the CPM (Cartesian parallel manipulator). The derived model also leads to decoupling dynamic characteristics, by which the complexity of the controller design can be significantly reduced. Based on this approach, a model-based computed torque method for positioning control of the CPM is illustrated. Both simulated and experimental results show that the model-based controller can achieve high positioning performance. Furthermore, it is shown that the coupling forces from other limbs play significant roles in the force components of the total dynamics of the CPM.

An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory

This paper analyzes the mobility and stiffness of a three-prismatic-revolute-cylindrical (3-PRC) translational parallel manipulator (TPM). Firstly, the original 3-PRC TPM is converted into a non-overconstrained manipulator since there exist some practical problems for the overconstrained mechanism. By resorting to the screw theory, it is demonstrated that the conversion brings no influences to the mobility and kinematics of the manipulator. Secondly, the stiffness matrix is derived intuitively via an alternative approach based upon screw theory with the consideration of actuations and constraints, and the compliances subject to both actuators and legs are taken into account to establish the stiffness model. Furthermore, the stiffness performance of the manipulator is evaluated by utilizing the extremum stiffness values over the usable workspace, and the influences of design parameters on stiffness properties are presented, which will be helpful for the architecture design of the TPM.

A three-DOF translational manipulator with decoupled geometry

A new 3-DOF translational parallel manipulator is presented in this paper. This manipulator has decoupled motion in for x, y, and z axes, and employs only revolute joints. The structure and kinematics of the manipulator are studied. The mechanism singularity is examined and the calibration methods are presented.

Kinematic Analysis and Design of a New 3-DOF Translational Parallel Manipulator

A new three degrees of freedom (3-DOF) translational parallel manipulator (TPM) with fixed actuators called a 3-PRC TPM is proposed in this paper. The mobility of the manipulator is analyzed via screw theory. The inverse kinematics, forward kinematics, and velocity analysis are performed and the singular and isotropic configurations are identified afterward. Moreover, the mechanism design to eliminate all singularities and generate an isotropic manipulator has been presented. With the variation on architectural parameters, the reachable workspace of the manipulator is generated and compared. Especially, it is illustrated that the manipulator in principle possesses a uniform workspace with a constant hexagon shape cross section. Furthermore, the dexterity characteristics are investigated in the local and global sense, respectively, and some considerations for real machine design have been proposed as well.