Translational Parallel Mechanism Research Articles

Structure Synthesis of 3-DOF Translational Parallel Mechanisms With Configurable Platform of Translation

Abstract The parallel mechanisms (PMs) with configurable platforms have the advantages of flexibility, high speed, and extra operability over PMs with common platforms. This paper proposes a systematic approach for synthesizing three-degrees-of-freedom (3-DOF) translational parallel mechanisms with configurable platforms of one translation DOF (TPMs-T) based on the finite screw. The motion relationship between the configurable platform and limbs is discussed to achieve the motion requirement of the TPMs-T limbs. The equivalence principle of kinematic joints is further pinpointed, and a series of lower mobility limbs have been developed. At last, the geometric relationship of assembly conditions is derived which can contribute to quickly solving the intersection of limb motions, a series of TPMs-T are constructed to verify the assembly conditions, and the fully controlled condition is discussed.

Disain CAD Mekanisme Paralel Tiga Derajat Translasi Murni Dengan Rantai Kinematik Kombinasi Sambungan Revolut dan Prismatik


 
 
 
 In this study it was discussed kinematic design of a 3-RRRPP translational parallel mechanism. The design was carried out by using simulation performed using CAD software. Motion platform was analyzed based on screw and reciprocal screw theory. The evaluation mechanism performance was determined by introducing the stages of research in the form to determine mechanism parts such as base, links, and platform. The work was continued with the assembly process of each part. Furthermore, kinematic response represented by displacement of platform positions was figured out by a CAD simulation. Based on the results of the simulation, it was successfully designed the mechanism performing the translational motion of the Platform.
 
 
 
 
 

Type Synthesis of Fully Decoupled Three Translational Parallel Mechanism with Closed-Loop Units and High Stiffness

In order to solve the problem of weak stiffness of the existing fully decoupled parallel mechanism, a new synthesis method of fully decoupled three translational (3T) parallel mechanisms (PMs) with closed-loop units and high stiffness is proposed based on screw theory. Firstly, a new criterion for the full decoupled of PMs is presented that the reciprocal product of the transmission wrench screw matrix and the output twist screw matrix of PMs is a diagonal matrix, and all elements on the main diagonal are nonzero constants. The forms of the transmission wrench screws are determined by the criterion. Secondly, the forms of the actuated and unactuated screws can be obtained according to their relationships with the transmission wrench screws. The basic decoupled limbs are generated by combination of the above actuated and unactuated screws. Finally, a closed-loop units construction method is investigated to apply the decoupled mechanisms in a better way on the high stiffness occasion. The closed-loop units are constructed in the basic decoupled limbs to generate a high-stiffness fully decoupled 3T PM. Kinematic and stiffness analyses show that the Jacobian matrix is a diagonal matrix, and the stiffness is obviously higher than that of the coupling mechanisms, which verifies the correctness of the proposed synthesis method. The mechanism synthesized by this method has a good application prospect in vehicle durability test platform.

Design and analysis of partially decoupled translational parallel mechanisms with single-loop structures

Design and analysis of partially decoupled translational parallel mechanisms with single-loop structures

Classification of 3-Degree-of-Freedom 3-UPU Translational Parallel Mechanisms Based on Constraint Singularity Loci Using Gröbner Cover

Abstract A 3-degree-of-freedom (DOF) 3-UPU translational parallel mechanism (TPM) is one of the typical TPMs. Despite comprehensive studies on 3-UPU TPMs in which the joint axes on the base and the moving platform are coplanar, only a few 3-UPU TPMs with skewed base and moving platform have been proposed, and the impact of link parameters on constraint singularity loci of such TPMs has not been systematically investigated. The advances in computing comprehensive Gröbner system (CGS) or Gröbner cover of parametric polynomial systems provide an efficient tool for solving this problem. This paper presents a systematic classification of 3-UPU TPMs with skewed base and moving platform based on constraint singularity loci. First, the constraint singularity equation of a 3-UPU TPM is derived. Using Gröbner cover, the 3-UPU TPMs are classified into 12 types. Finally, a novel 3-UPU TPM is proposed. Reconfiguration analysis shows that unlike most existing 3-UPU TPMs which can transit from a 3-DOF translational mode to two or more 3-DOF operation modes, the proposed 3-UPU TPM can only transit from a 3-DOF translational mode to one general 3-DOF operation mode. The singularity locus divides the workspace of this 3-UPU TPM into two constraint singularity-free regions. As a by-product, a 3-UPU parallel mechanism that the moving platform can undergo 3-DOF translation and 1-DOF infinitesimal rotation is revealed. This work provides a solid foundation for the design of 3-UPU TPMs and a starting point for the classification of 3-UPU parallel mechanisms.

Dynamic performance evaluation of the parallel mechanism for a 3T2R hybrid robot

The performance measurements for the parallel manipulator can be divided into kinematic and dynamic indexes. The kinematic estimations have been well explored and contributed in the parallel structure selection, singularity avoidance and dimension synthesis. The dynamic performance assessments will also have significant contributions for parallel robots. In this research, the complete inverse dynamic model is formulated via the Lagrangian approach and verified by the simulation results. Two novel dynamic indices are proposed to explore the coupled inertia features among different kinematic limbs. The multiple dynamic indices are analyzed and compared on two translational parallel mechanisms with similar joint configurations. A feasible controller is provided to track the desired trajectory of the mobile platform.

Kinematic design of a translational parallel mechanism based on sub-kinematic chain determined workspace superposition

This paper presents the kinematic design of a translational parallel mechanism (PM) named Vari-Orthoglide by means of the workspace superposition, according to the sub-kinematic chain (SKC) based PM composition principle. The main topological characteristics of the manipulator with two SKCs under study, such as the position and orientation (POC) characteristics, degree of freedom (DOF) and coupling degree are analyzed, which turns out that the coupling degree equals to 1, implying the partially decoupled motion. With the topological characteristics based kinematic modeling principle, a symbolic model of the kinematics is established to derive its symbolic direct and inverse kinematic solutions. Based upon the direct kinematic solution, the workspaces for the two SKCs can be efficiently found. Moreover, the singularity loci are identified for finding the singularity-free workspace, where a regular workspace is fitted as the task workspace as expected. The presented work shows an approach to design translational parallel mechanisms considering motion decoupling and regular workspace, applicable to other types of parallel mechanisms.

Enumeration and optimum design of a class of translational parallel mechanisms with prismatic and parallelogram joints

Spatial joints (Hooke and spherical joint) generally limit parallel manipulator's motion range and performance, while higher performance will be achieved when applying more planar pairs (prismatic and revolute joint), which can promise small movement constraints and high stiffness. In this paper, a novel design method for three translational degrees of freedom parallel mechanisms containing prismatic joints and parallelogram units ((R-R)2 linkage) is proposed by mapping relationship with augmented matrices of upper triangular matrix. All these mechanisms can be assembled quickly with modular parts and most of which are partially decoupled. In this study, one of these proposed structures is taken as an example for developing a redundant manipulator. Based on vector-loop equations, its position model is derived and the singular configurations are investigated. Kinematic and static performance of this architecture are conducted, as well as the multi-objective optimization is implemented using Genetic Algorithm.

Investigation of 2-DOF Compliant Translational Parallel Mechanism and Applied in the Docking Device

Investigation of 2-DOF Compliant Translational Parallel Mechanism and Applied in the Docking Device

A calibration method for overconstrained spatial translational parallel manipulators

Abstract A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90% are achievable.

On the Maximization of Joint Velocities and Generalized Reactions in the Workspace and Singularity Analysis of Parallel Mechanisms

SummaryAn approach for calculating the maximum possible absolute values of joint velocities or generalized reactions in a leg of a parallel mechanism has been considered in this paper. The Jacobian analysis and the Screw theory-based methods have been used to acquire the result. These values are calculated for the “worst” directions of the external load or end-effector’s velocity for each leg. The feasibility of using these parameters as the measures of closeness to different types of parallel mechanism singularity is discussed. Further, how this approach is related to the state-of-the-art methods has been illustrated. The key aspect of the discussed approach is that the normalization of vectors or screws is carried out separately for angular and linear components. One possible advantage of such an approach is that it deals only with the kinematic and statics of the mechanism while still providing physically meaningful and practically applicable measures. Case studies of a 3-Degrees Of Freedom translational parallel mechanism and a planar parallel mechanism are presented for illustration and comparison.

Type Synthesis of Parallel Mechanisms With a Constant Jacobian Matrix

Jacobian matrix plays a key role in the analysis, design, and control of robots. For example, it can be used for the performance analysis and evaluation of parallel mechanisms (PMs). However, the Jacobian matrix of a PM generally varies with the poses of the moving platform in the workspace. This leads to a nonconstant performance index of the PM. PMs with a constant Jacobian matrix have simple kinematics and are easy to design and control. This paper proposes a method for obtaining PMs with a constant Jacobian matrix. First, the criteria for detecting invariance of a Jacobian matrix are obtained based on the screw theory. An approach to the synthesis of PMs with a constant Jacobian matrix is then proposed. Using this approach, PMs with a constant Jacobian matrix are synthesized in two steps: the limb design and the combination of the limbs. Several PMs with a constant Jacobian matrix are obtained. In addition to the translational parallel mechanisms (TPMs) with a constant Jacobian matrix in the literature, the mixed-motion PMs whose moving platform can both translate and rotate with a constant Jacobian matrix are newly identified. The input/output velocity analysis of several PMs is presented to verify that Jacobian matrix of these PMs is constant.

Intuitive Physical Human-Robot Interaction: Using a Passive Parallel Mechanism

In this article, we propose a novel passive mechanism and a macro?mini architecture for effective and intuitive physical human?robot interaction (pHRI). The macro?mini concept allows the use of a mini low-impedance passive (LIP) mechanism to effortlessly and intuitively control a macro high-impedance active (HIA) system such as a gantry manipulator. The proposed mini LIP design is based on a three-degrees-of-freedom (3-DoF) translational parallel mechanism, which makes it simple and compact, thereby adding little inertia to the end-effector of the macro HIA mechanism.

Design of a Spatial Translation Mechanism by Optimizing Spatial Ground Structures and Its Kinematic Analysis

In our previous work, we designed a three-degrees-of-freedom (3DOF) translational parallel mechanism based on a proposed design strategy. In this paper, the design strategy is further improved, and a novel spatial translation mechanism (STM) is found. The novel STM consists of a platform, a base, and six modules between the platform and the base. Each module is a passive planar 6R single-loop closed chain, and it is connected with two other modules. Meanwhile, three modules are connected to the base, and the other three modules are connected to the platform. All the connections among the modules, platform, and base are realized by revolute joints. There are no obvious limbs in the mechanism due to the complex connections. The mobility of the STM is analyzed, and the forward kinematics is investigated. To validate the effectiveness and feasibility of the design, one prototype is fabricated. At the end of the paper, we draw some conclusions and discuss the future works.

Position-Space-Based Design of a Symmetric Spatial Translational Compliant Mechanism for Micro-/Nano-Manipulation.

Symmetry enables excellent motion performance of compliant mechanisms, such as minimized parasitic motion, reduced cross-axis coupling, mitigated buckling, and decreased thermal sensitivity. However, most existing symmetric compliant mechanisms are heavily over-constrained due to the fact that they are usually obtained by directly adding over-constraints to the associated non-symmetric compliant mechanisms. Therefore, existing symmetric compliant mechanisms usually have relatively complex structures and relatively large actuation stiffness. This paper presents a position-space-based approach to the design of symmetric compliant mechanisms. Using this position-space-based approach, a non-symmetric compliant mechanism can be reconfigured into a symmetric compliant mechanism by rearranging the compliant modules and adding minimal over-constraints. A symmetric spatial translational compliant parallel mechanism (symmetric XYZ compliant parallel mechanism (CPM)) is designed using the position-space-based design approach in this paper. Furthermore, the actuation forces of the symmetric XYZ CPM are nonlinearly and analytically modelled, which are represented by the given primary translations and the geometrical parameters. The maximum difference, between the nonlinear analytical results and the nonlinear finite element analysis (FEA) results, is less than 2.58%. Additionally, a physical prototype of the symmetric XYZ CPM is fabricated, and the desirable motion characteristics such as minimized cross-axis coupling are also verified by FEA simulations and experimental testing.

Systematic Approach to the Design of Spatial Translational Compliant Parallel Mechanisms

Systematic Approach to the Design of Spatial Translational Compliant Parallel Mechanisms

KINEMATICS AND WORKSPACE ANALYSIS OF A 3 DEGREE OF FREEDOM PARALLEL MECHANISM WITH PARALLELOGRAM LINKAGE

In this paper, a 3-DOF translational parallel mechanism with parallelogram linkage was studied. According to the space vector relation between the moving platform and the fixed base, the direct and inverse position solutions of this mechanism was deduced through analytical method. In addition, the error of the algorithm was analyzed, and the algorithm had turned out to be effective and to have the satisfactory computational precision. On the above basis, the workspace of this mechanism was found through graphical method, which was compared with that of finding through Monte Carlo method, and there was the feasibility for analyzing the workspace of the mechanism by graphical method. The characteristic of the mechanism was analyzed by comparing the results of two analysis methods, which provided a theoretical basis for the application of the mechanism.

Type synthesis of 1T2R and 2R1T parallel mechanisms employing conformal geometric algebra

Abstracts This paper proposes an analytical method based on conformal geometrical algebra to implement and unify type synthesis of one translational and two rotational (1T2R) parallel mechanisms and two rotational and one translational (2R1T) parallel mechanisms. Firstly, conformal geometrical algebra is introduced in this paper to describe finite motions and carry out type synthesis of parallel mechanisms in an algebraic way. Secondly, the finite motions of 1T2R and 2R1T parallel mechanisms are described and their relations are explored, and this results in unifying the type synthesis of these two types of parallel mechanisms in the same procedure. Then, a parametric and algebraic generation method is proposed to obtain available limbs and axes layout of joints with these limbs. Finally, the assembly conditions among available limbs are given to synthesize systematically 2R1T parallel mechanisms with non-overconstrained or overconstrained property, as well as 1T2R parallel mechanisms with the same properties. This method proposed in this paper is valid in carrying out finite motion representation and type synthesis of parallel mechanisms in an algebraic and analytical way, and then is beneficial to an automatic manner using computer programming languages. Furthermore, the method may solve type synthesis of special parallel mechanisms, such as parallel mechanisms with varied output rotational axes.

An experimental study on the direct & indirect dynamic identification of an over-constrained 3-DOF decoupled parallel mechanism

This paper provides the state of the art of obtaining the dynamic model of an over-constrained 3-DOF translational parallel mechanism, namely, Tripteron, by performing system identification concept in which friction is taken into account. To this end, as the first step, in order to circumvent the problem of being over-constrained, i.e., inconsistent numbers of equations and unknown parameters in the dynamic model, some modifications on the kinematic arrangement of the constituted limbs are applied, in such a way that preserve the degrees-of-freedom performed by the mechanism under study, the so-called Tripteron with three translational degrees-of-freedom. Then, in order to have a close-to-reality dynamic model, the model is combined with the model of the linear module friction. Afterward, by using the practical data, the optimum values for the uncertain parameters of the inverse dynamic and friction models are obtained by a white-box identification approach based on Genetic algorithm. In addition, in order to propose a less complex model, a model based on the polynomial regressors of position, velocity, acceleration and applied torque of each axis is proposed. Finally, by proposing some criterion, the paper concludes by a comprehensive discussion on the performance of the obtained models.

Structural design of a novel family of 2-DOF translational parallel robots to enhance the normal-direction stiffness using passive limbs

Many planar 2-DOF translational parallel robots which were invented for the simple industrial tasks are easy to suffer the problem of the poor intrinsic stiffness along the normal direction to the plane of motion. To solve this problem, the passive limbs can be introduced into the design of parallel mechanisms to increase the stiffness and stability of the robots. Besides the capability of stiffness increasing, the passive limbs can also provide constraints, generate decoupled configuration, bear full or partial weights and/or payloads, liberate constraints from the actuations, and even decrease the required actuating forces of active limbs. However, there is still no systematic study on the utilization of passive limbs to date. In this paper, the stiffness–robust 2-DOF translation parallel robots with passive limbs are investigated in terms of type synthesis. Based on the distribution of wrench system among the active limbs and passive limbs, a full-scale criterion is developed for effectively and efficiently synthesizing all kinds of 2-DOF translational parallel mechanisms with one or more passive limbs. All 14 types of the 2-DOF translational parallel mechanisms with passive limbs are synthesized and exemplified through kinematic diagrams. A qualitative stiffness index is purposed to evaluate the stiffness performance of all of the synthesized configurations directly and rapidly. Finally, an optimized configuration of stiffness-enhanced 2T PM is derived and exhibits the best stiffness performance.