Translational Parallel Mechanism Research Articles

Determination and Synthesis of Translational Parallel Mechanism with Constant Jacobian Matrix

Determination and Synthesis of Translational Parallel Mechanism with Constant Jacobian Matrix

THREE-DOF TRANSLATIONAL PARALLEL MECHANISM PARTLY COMPOSED OF WIRES

This paper proposes a low-weight parallel mechanism, partly composed of wires instead of rigid links, which combines a parallel mechanism and a wire-driven parallel mechanism. The proposed mechanism does not require actuators to maintain wire tensions, as is the case in general parallel wire-driven mechanisms, because the proposed mechanism maintains wire tension using constant force springs attached to the base plate. Additionally, the proposed mechanism is compliant due to the wires and the proposed mechanism is relatively safe because a output link of the mechanism does not fall immediately after exceeding a maximum payload. In this paper, we derive the static relations of the proposed mechanism through a balance of forces and moments and establish the feasibility of the proposed mechanism through positioning and maximum payload tests performed on a prototype of the proposed mechanism.

Constant motion/force transmission analysis and synthesis of a class of translational parallel mechanisms

Motion/force transmission is one of the most important issues and the foundation of analysis and optimal design in the field of parallel mechanisms. It reflects the capacity that each limb in a parallel mechanism transmits its driving force to the moving platform and also the output capacity of the moving platform under definite input of the limb. Several performance indices were proposed to measure motion/force transmission. However, they are instantaneous values varying with different poses. In this paper, a criterion for constant power transmission and the excellent motion/force transmission occurring within a class of translational parallel mechanisms in different poses is proposed based on screw theory. To obtain the translational parallel mechanisms with constant and excellent motion/force transmission, a host of configurations are synthesized based on constraint screw theory when the criterion is met. The criterion proposed in this paper is expected to be applied for the translational parallel mechanisms to analyzing motion/force transmission and optimizing the design.

A finite screw approach to type synthesis of three-DOF translational parallel mechanisms

This paper for the first time presents a finite screw approach to type synthesis of three-degree-of-freedom (DOF) translational parallel mechanisms (TPMs). Firstly, the finite motions of a rigid body, a TPM and its limbs are described by finite screws. Secondly, given the standard form of a limb with the specified DOF, the analytical expressions of the finite screw attributed to the limb are derived using the properties of screw triangle product, resulting in a full set of the 3-, 4- and 5-DOF limbs that can readily be used for determining all the potential topological structures of TPMs. Finally, the assembly conditions for type synthesis of TPMs are proposed by taking into account the inclusive relationship between the finite motions of a TPM and those of its limbs. The merit of this approach lies in that the limb structures can be formulated in a justifiable manner that naturally ensures the full cycle finite motion pattern specified to the moving platform.

一种新型3-CRU并联机构的动力学建模

3-CRU平动并联机构具有3条CRU支链组，具有三个运动方向上的平动特性，对于目前多数并联机构需要较少自由度这一现状以及在生产中的实际情况，本文根据广发的调查取证，设计并验证了一种全新的3-CRU平动并联机械手，在对机构进位置和速度分析的基础上，得到新机构的第一阶影响系数矩阵，继而采用虚功法建立新型3-CRU平动并联机构运动平台的动力学模型，为精密机构平台的精度划分提供帮助。 This 3-CRU parallel mechanism has three CRU branched chain groups and this parallel mechanism has three characteristics of translational movement direction. In practical application, it does not require so much degree of freedom. Based on the investigation and collecting data, the device needs low degree of freedom. A novel 3-CRU translational parallel mechanism has been designed for adapting to this situation. In this paper, the position and speed of the mechanism are analyzed, and the Jacobi matrix of the mechanism has been obtained. According to the principle of virtual work, we established the kinetic model of 3-CRU translational parallel mechanism. It can provide the help for the researching on the accuracy of precision motion platform.

Analysis of Translational Parallel Mechanism with Good Motion/force Transmissibility

Analysis of Translational Parallel Mechanism with Good Motion/force Transmissibility

Kinematic analysis of a 6R single-loop overconstrained spatial mechanism for circular translation

This paper deals with the kinematic analysis of a double-spherical 6R and parallelogram 4R based single degree-of-freedom overconstrained 6R spatial mechanism for circular translation (DSPB6RCT). How to construct a DSPB6RCT is recalled first. A closed-form solution to the kinematic analysis of the mechanism is then discussed in detail. The kinematic analysis of the mechanism is reduced to the solution of a univariate quadratic equation. The self-motion of a DSPB6RCT is further investigated. The analysis shows that a DSPB6RCT usually has two solutions to the kinematic analysis for a given input. Numerical examples demonstrate that this class of mechanisms may have 0, 2 or 4 full-turn revolute joints and one or two circuits (closure modes or branches). This work provides a solid starting point for further investigation on the classification and application of DSPB6RCTs as well as the kinematic analysis of other classes of overconstrained 6R spatial mechanisms for circular translation. The results can also be used for the type synthesis and singularity analysis of translational parallel mechanisms.

Type Synthesis of Three-Degree-of-Freedom Translational Compliant Parallel Mechanisms

In this paper, we apply screw theory to type synthesis of compliant parallel mechanisms (PMs) with translational degree-of-freedom (DOF). Compliant PMs are formed by a moving platform supported by three or more limbs each of which is a serial chain of flexure joints and rigid bodies. They achieve movement through the deformation of flexure joints and have been widely used in precision machinery. As an important task in the conceptual design stage, the goal of type synthesis is to determine the chain of each limb as well as their relationship when they are assembled in parallel for a prescribed motion pattern. In our approach, we study a category of commonly used flexure primitives and flexure elements whose freedom and constraint spaces are characterized by twists and wrenches in screw theory. Following the well-studied synthesis procedure for rigid body PMs, we propose a synthesis procedure for compliant PMs via screw theory. As an example, we demonstrate the procedure for synthesizing compliant PMs with three translational DOF. Tables of limbs, types, and geometric conditions for the assemblies of these limbs are presented. The paper provides a catalog of 3DOF translational compliant PM designs. At last, we developed finite element simulation to validate one of the synthesized designs.

Design of decoupled, compact, and monolithic spatial translational compliant parallel manipulators based on the position space

The initial version of this paper was presented at 2014 Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Tianjin, China. The conceptual design of three types of decoupled, compact, and monolithic XYZ compliant parallel manipulators (CPMs) is taken into account in this paper using the position space concept. The CPMs are termed CUBEs due to the shape of their compact structures. The position space of a compliant module is the combination of all permitted positions in an XYZ CPM system where the constraint of this compliant module in the XYZ CPM system remains unchanged when the position of the compliant module changes within the position space. The position of each compliant P joint is considered relative to its adjacent compliant joint/module rather than being considered in insolation. A design method for obtaining monolithic XYZ CPMs is proposed in terms of both the kinematic substitution and position spaces. Three types of monolithic XYZ CPMs are then demonstrated using the proposed method, with the help of three classes of kinematically decoupled three degrees of freedom translational parallel mechanisms. These monolithic XYZ CPMs include a 3- PPP (P: prismatic) XYZ CPM, a 3- PPPR (R: revolute) XYZ CPM, and a 3- PPPRR XYZ CPM. The position space concept can enable the system configurations to be designed based on the chosen optimization requirements, which include considerations such as compactness or minimization of parasitic rotations. This provides an efficient and systematic method to arrange the relative position between any two compliant joints/modules so that one can easily generate practical and useful configurations for XYZ CPMs. The resulting XYZ CPM is the most compact one when the fixed ends of the three actuated compliant P joints thereof overlap or are as close to each other as possible.

Kinematic analysis of a novel 3-CRU translational parallel mechanism

Abstract. In this paper, a modified 3-DOF (degrees of freedom) translational parallel mechanism (TPM) three-CRU (C, R, and U represent the cylindrical, revolute, and universal joints, respectively) structure is proposed. The architecture of the TPM is comprised of a moving platform attached to a base through three CRU jointed serial linkages. The prismatic motions of the cylindrical joints are considered to be actively actuated. Kinematics and performance of the TPM are studied systematically. Firstly, the structural characteristics of the mechanism are described, and then some comparisons are made with the existing 3-CRU parallel mechanisms. Although these two 3-CRU parallel mechanisms are both composed of the same CRU limbs, the types of freedoms are completely different due to the different arrangements of limbs. The DOFs of this TPM are analyzed by means of screw theory. Secondly, both the inverse and forward displacements are derived in closed form, and then these two problems are calculated directly in explicit form. Thereafter, the Jacobian matrix of the mechanism is derived, the performances of the mechanism are evaluated based on the conditioning index, and the performance of a 3-CRU TPM changing with the actuator layout angle is investigated. Thirdly, the workspace of the mechanism is obtained based on the forward position analysis, and the reachable workspace volume is derived when the actuator layout angle is changed. Finally, some conclusions are given and the potential applications of the mechanism are pointed out.

Type Synthesis of Single-Loop Overconstrained 6R Spatial Mechanisms for Circular Translation

To discover single-degree-of-freedom (DOF) single-loop overconstrained mechanisms is still an open problem. This paper deals with the type synthesis of single DOF single-loop overconstrained 6RMCTs (6R spatial mechanisms for circular translation). These mechanisms provide alternatives to planar parallelograms and are also associated with self-motion of several translational parallel mechanisms. 6RMCTs are to be obtained using a construction approach in combination with the approaches to the type synthesis of parallel mechanisms. By imposing certain conditions on the hybrid overconstrained 6R (plano-spherical, plano-Bennett, double-spherical, and spherico-Bennett) mechanisms, Bricard plane symmetric mechanism, and Bricard line symmetric mechanism, six special cases of 6RMCTs are obtained. By combining planar parallelograms with these special mechanisms, the general cases of 6RMCTs are then constructed. Finally, 4R2H, 2R4H, and 6H mechanisms for circular translation are obtained from the above 6RMCTs by replacing one or more pairs of R (revolute) joints with parallel axes each with a pair of H (helical) joints with parallel axes and the same pitch. This work contributes to the research on overconstrained six-bar mechanisms and further reveals that the research areas of parallel mechanisms and single-loop overconstrained mechanisms are closely related.

Conceptual designs of multi-degree of freedom compliant parallel manipulators composed of wire-beam based compliant mechanisms

This paper proposes conceptual designs of multi-degree(s) of freedom (DOF) compliant parallel manipulators (CPMs) including 3-DOF translational CPMs and 6-DOF CPMs using a building block based pseudo-rigid-body-model (PRBM) approach. The proposed multi-DOF CPMs are composed of wire-beam based compliant mechanisms (WBBCMs) as distributed-compliance compliant building blocks (CBBs). Firstly, a comprehensive literature review for the design approaches of compliant mechanisms is conducted, and a building block based PRBM is then presented, which replaces the traditional kinematic sub-chain with an appropriate multi-DOF CBB. In order to obtain the decoupled 3-DOF translational CPMs (XYZ CPMs), two classes of kinematically decoupled 3-PPPR (P: prismatic joint, R: revolute joint) translational parallel mechanisms (TPMs) and 3-PPPRR TPMs are identified based on the type synthesis of rigid-body parallel mechanisms, and WBBCMs as the associated CBBs are further designed. Via replacing the traditional actuated P joint and the traditional passive PPR/PPRR sub-chain in each leg of the 3-DOF TPM with the counterpart CBBs (i.e. WBBCMs), a number of decoupled XYZ CPMs are obtained by appropriate arrangements. In order to obtain the decoupled 6-DOF CPMs, an orthogonally-arranged decoupled 6-PSS (S: spherical joint) parallel mechanism is first identified, and then two example 6-DOF CPMs are proposed by the building block based PRBM method. It is shown that, among these designs, two types of monolithic XYZ CPM designs with extended life have been presented.

Design of 3-legged XYZ compliant parallel manipulators with minimised parasitic rotations

SUMMARYThis paper deals with the design of 3-legged distributed-compliance XYZ compliant parallel manipulators (CPMs) with minimised parasitic rotations, based on the kinematically decoupled 3-PPPRR (P: prismatic joint, and R: revolute joint) and 3-PPPR translational parallel mechanisms (TPMs). The designs are firstly proposed using the kinematic substitution approach, with the help of the stiffness center (SC) overlapping based approach. This is done by an appropriate embedded arrangement so that all of the SCs associated with the passive compliant modules overlap at the point where all of the input forces applied at the input stages intersect. Kinematostatic modelling and characteristic analysis are then carried out for the proposed large-range 3-PPPRR XYZ CPM with overlapping SCs. The results from finite element analysis (FEA) are compared to the characteristics found for the developed analytical models, as are experimental testing results (primary motion) from the prototyped 3-PPPRR XYZ CPM with overlapping SCs. Finally, issues on large-range motion and dynamics of such designs are discussed, as are possible improvements of the actuated compliant P joint. It is shown that the potential merits of the designs presented here include a) minimised parasitic rotations by only using three identical compliant legs; b) compact configurations and small size due to the use of embedded designs; c) approximately kinematostatically decoupled designs capable of easy controls; and d) monolithic fabrication for each leg using existing planar manufacturing technologies such as electric discharge machining (EDM).

A novel 4-UPU translational parallel mechanism with fault-tolerant configurations

This paper aims at designing a pure translational parallel mechanism constructed by UPU (universal-prismatic-universal joint) kinematic limbs. First, the typical problem of unexpected rotations is pointed out from analyzing the typical 3-UPU parallel mechanism, and the reason for unexpected rotations of parallel mechanism constructed by UPU kinematic limbs is analyzed. Then, in order to design a pure translational parallel mechanism constructed by UPU without the unexpected rotations, the 2-UPU single loop is chosen as the basic structure to construct the 4-UPU translational parallel mechanism. Each 2-UPU single loop can be used to constrain a rotation about an axis of the linear complexes, which defined the unexpected rotations. Therefore, a novel type of 4-UPU pure translational parallel mechanism with redundant actuations is proposed. Since the existence of redundantly actuated kinematic limb, this proposed parallel mechanism possesses analytical forward kinematics, and its singularity can be avoided completely. Finally, the workspace and fault-tolerant performance are analyzed. When the proposed 4-UPU parallel mechanism is located in a fault-tolerant configuration, the moving platform can still possess movable ability to realize the given task even if one kinematic limb is in locked-joint failure mode, and the fault-tolerant workspace is obtained.

Some aspects of topology and kinematics of a 3DOF translational parallel mechanism

The paper presents elements of the topology, geometry and the kinematic analysis of a translational parallel mechanism with three degrees of freedom. In such mechanisms the selection of a proper structure and geometry ensures that the driven link maintains a fixed orientation relative to the base. The method of determination of the configuration of mechanisms using contour vector notation was elaborated in the paper. The equations for the analysis of the direct and inverse kinematics task are determined. An analytical procedure for determining the system’s singular positions is presented and illustrated with examples

Novel design solution to high precision 3 axes translational parallel mechanism

The paper presents a 3 degree of freedom UPU mechanism having an excellent practical feasibility. The mathematical model and the design considerations of the 3-UPU mechanism are discussed. A detailed sensitivity analysis is carried out and the results are discussed in a new perspective. A novel design solution for a high precision three axis translation parallel mechanism is presented. We describe and validate the theoretical observations with the prototype model. The capability of the 3-UPU mechanism in performing fine motion manipulation, high precision trajectory following and metrological measurement is demonstrated. The performances of the 3-UPU mechanism concur with the theoretical observations in contrast to what is presented in previous works.

Workspace Analysis and Parameter Optimization of 3-DOF Parallel Mechanism

A spatial 3-DOF translational parallel mechanism is analyzed. Its inverse kinematic model is established. The section view of the workspace of the parallel mechanism is presented via boundary search method under the defined constraints. Considering the workspace volume as the optimization object, the relationship between structural parameters and workspace volume is obtained and the structural parameters to be optimized are determined. Finally, the optimization configuration of the mechanism is obtained. The results show that the volume of the workspace increases 1.55 times as much as the original volume, which lay the foundation for the architecture design.

Accuracy Analysis of 3-UPU Translational Parallel Robot Mechanism

According to the inverse solutions of 3-UPU translational parallel robot mechanisms, in which both the base and the mobile platform are triangle and similar to each other, the accuracy model of parallel robot mechanisms is established by the differentiation of the kinematic. The effects of length error of driving poles, structure size change and posture change on the accuracy of robot are studied by simulations,which provided the foundation for practical error compensating and controlling of the mechanism.

Topology and analysis of the singularities of a parallel mechanism with three degrees of freedom

This paper describes the topology, geometry and kinematics of a translational parallel mechanism with three degrees of freedom. Basic topological and geometric conditions for ensuring exclusively translational motion of the driven link relative to the base are formulated. Fundamental relations for the kinematic analysis of the system are introduced. The equations are needed to describe and solve the direct and inverse problem of the kinematics and to provide a basis for the analytical definition of the mechanism's singular configurations and their determination.

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.