3T1R Parallel Manipulator Research Articles

Kinematics and compliance analyses of a 3T1R parallel manipulator with rotational symmetry

Pick-and-place automation requires manipulators to have at least three translational (3T) and one rotational (1R) degrees of freedom. Parallel manipulators usually include four limbs connected to a traveling plate to generate 3T1R motion. For the four limbs to be arranged with rotational symmetry, complicated types of passive joints and traveling plates are required, which make 3T1R manipulators structurally weaker and prone to wear and clearance issues. This paper presents a new 3T1R parallel manipulator that uses only revolute joints as the active and passive joints. Compared with other joint types, revolute joints are structurally simpler and stronger. They have an unlimited range of motion and can be preloaded to eliminate clearance. The proposed manipulator allows the four limbs to be connected to a simple H-shaped traveling plate with rotational symmetry. Kinematic analysis shows that the new 3T1R manipulator has a homogenous workspace with a high workspace-to-footprint ratio. Compliance analysis and experiments are given to verify that the manipulator can achieve low and homogenous compliance. The proposed manipulator is expected to provide an alternative in pick-and-place applications.

2PPaRR-2PPaRU: Design, analysis, and optimization of a new 3T1R parallel manipulator with rotational pitch motion

A new 3T1R parallel manipulator (PM) 2PPaRR-2PPaRU with rotational pitch motion is proposed in this paper. In such a mechanism, there are four limbs connected to the moving platform (MP) through several revolute joints and universal joints, and all actuated joints are prismatic joints with an axis along a vertical direction. Mobility and motion characteristics are verified by constraint screw theory. The inverse kinematic solutions and the singularity configurations are derived through kinematic analysis. Next, the workspace analysis and the connection between [Formula: see text] and the volume of the reachable workspace are performed. The local motion/force transmission index is selected to evaluate the local transmission performance of 2PPaRR-2PPaRU PM. Finally, the global motion/force transmission index and the volume of reachable workspace are considered simultaneously to optimize the structural parameters. The 2PPaRR-2PPaRU PM with improved local transmission performance and reachable workspace has been achieved after optimization.

TetraFLEX: Design and kinematic analysis of a novel self‐aligning family of 3T1R parallel manipulators

AbstractA new family of 3T1R parallel manipulators (PMs) with self‐aligning property, named TetraFLEX, is presented. 3T1R manipulators have many applications in different fields. Moreover, self‐aligning property refers to the presence of passive joints in the PM limbs that are conceived to compensate for possible misalignments between the sliding directions of the actuated prismatic(P)‐pairs. This property allows the fixation of the limbs in different frame geometries. Thus, this advantage broadens the PM applications to field robotics in several scenarios. Here, the position and singularity analyses of the new family of self‐aligning PMs is addressed with a unified approach. The results are that both the direct and the inverse position analyses have simple closed‐form solutions and that wide free‐from‐singularity regions of TetraFLEX PMs' workspace exist. The effectiveness of the technical proposal is also illustrated by discussing their design criteria and kinetostatics performances in a case study.

Kinematics analysis and workspace optimization for a 4-DOF 3T1R parallel manipulator

A four degrees-of-freedom (DOF) Parallel Manipulator (PM) with a 4PPa-2PaR configuration has been proposed to generate 3-DOF Translational and 1-DOF Rotational (3T1R) motions in our early work. It has the advantages of symmetric geometry, simple kinematics and infinite extension of translational workspace along its linear guide direction. However, its V-type assembly mode results in a long distance between its moving platform and the base, which makes its stiffness and accuracy lower. Besides, its the other two translational workspaces are limited due to its kinematic singularities. To overcome such limitations, the PM is modified by utilizing its M-type assembly mode and placing an offset angle to the last parallelogram mechanism. To simplify the displacement analysis, a geometrical projection method is employed, while a closed-loop vector approach is used for its instantaneous kinematic analysis. Both singularity and workspace issues are investigated. An optimization algorithm based on Genetic Algorithm is proposed to maximize the reachable workspace. The optimization result indicates that the workspace is significantly increased. A prototype of the M-type PM is fabricated to validate the effectiveness of the modified design.

Classification of a 3-RER Parallel Manipulator Based on the Type and Number of Operation Modes

Abstract The type/number of operation modes of a parallel manipulator (PM) may vary with the link parameters of the PM. This paper presents a systematic classification of a 3-RER PM based on the type/number of operation modes. Here, R and E denote revolute joint and planar joint, respectively. The 3-RER PM was proposed as a 4-degree-of-freedom (DOF) 3T1R PM in the literature. Using the proposed method, classification of a PM based on the type/number of operation modes can be carried out in four steps, including formulation of constraint equations of the PM, preliminary classification of the PM using Gröbner cover, operation mode analysis of all the types of PMs using primary decomposition of ideals, and identification of redundant types of PMs. The classification of the 3-RER PM shows that it has 13 types. Besides the two 4-DOF 3T1R operation modes, different types of 3-RER PMs may have up to two more 3-DOF or other types of 4-DOF operation modes. Motion characteristics of the moving platform of 3-RER PMs are also identified using Euler parameter quaternions. This work is the first systematic study on the impact of link parameters on the operation modes of the 3-RER PM and provides a solid foundation for further research on the design and control of 3-RER PMs and other multi-mode (or reconfigurable) PMs.

Influence-Coefficient Method for Identifying Maximum-Load Configurations and Variable-Load Issues in Manipulators

The dimensioning of general-purpose machines such as manipulators involves the solution of a number of preliminary issues. The determination of reference external loads and the identification of machine configurations that give the maximum internal load for each component are two of these issues. These two problems are commonly addressed through trial-and-error procedures based on dynamic modelling, which are implemented with the support of simulation software, since static analyses are commonly considered inadequate to solve them. Despite this, here, a technique based on influence coefficients and static analyses is presented which solves them. Such technique is also able to foresee and justify dynamic issues (i.e., possible vibrations, etc.) that could heavily affect the machine behavior. The effectiveness of the proposed technique is proved by implementing it on a 3T1R parallel manipulator. The presented design method is general and applicable to any type of non-overconstrained manipulator or mechanism.

Unified formulas of constrained Jacobian and Hessian matrices for 3T1R overconstrained parallel mechanisms

The article proposes a general approach for solving the unified formulas of the constrained Jacobian matrix and constrained Hessian matrix of three translational and one rotational (3T1R) parallel manipulators (PMs). First, based on the constraint properties of PMs, the constrained couples of the limbs are divided into two categories: invariable and variable constrained couples. The unified 2 × 6 constrained Jacobian matrix and 2 × 6 × 6 constrained Hessian matrix of the 3T1R PM are established. Then, a typical 2-(UPU)2R PM is selected, and the 6 × 6 Jacobian matrix and 6 × 6 × 6 Hessian matrix of the mechanism are deduced. The singularity of the mechanism is analyzed based on the 6 × 6 Jacobian matrix. Finally, the kinematics are derived, and results demonstrating the proposed method were provided.

A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

New 3T1R Parallel Manipulator 2-(RPa3R)3R with Zero Coupling Degree and Partial Decoupling: Design and Kinematics

New 3T1R Parallel Manipulator 2-(RPa3R)3R with Zero Coupling Degree and Partial Decoupling: Design and Kinematics

Kinematics, singularity, and optimal design of a novel 3T1R parallel manipulator with full rotational capability

Parallel manipulators (PMs) with 3T1R (three translational and one rotational degrees of freedom) or Schonflies motion are very useful in industry. However, most 3T1R PMs have a limited range of rotation less than 90° while many practical tasks require a large range of rotation over 180°. Furthermore, there are no 3T1R PMs with full rotational capability that has small number of single-DOF joints and fixed actuators. A novel 2-(RRR)2RH PM with full rotational capability is proposed, where R and H denote a revolute joint and a helical joint, respectively. The moving platform is connected to the fixed base by two identical (RRR)2RH chains, where (RRR)2 denotes a 2- RRR closed chain. First, kinematic analysis of the proposed 2-(RRR)2RH PM, including mobility analysis, inverse and direct kinematics, singularity analysis, and workspace is presented. Second, the local conditioning index is used to evaluate the kinematic performance of the PM. Finally, optimal kinematic design of the 2-(RRR)2RH PM is investigated. The 2-(RRR)2RH PM has only 16 single-DOF joints and can be actuated by four fixed revolute joints. These features make it a good candidate in many applications.

Kinematics Analysis of a Novel 3T1R Parallel Manipulator with Full Rotational Capability

Kinematics Analysis of a Novel 3T1R Parallel Manipulator with Full Rotational Capability

Kinematic analysis and design of a novel 3T1R 2-(PRR)2RH hybrid manipulator

A 4-DOF (degrees of freedom) parallel manipulator with three translations and one rotation (3T1R) is very useful in industry. Most of the 3T1R parallel manipulators have limited rotational capabilities that usually have a range less than 90°. A novel 3T1R 2-(PRR)2RH hybrid manipulator with full rotational capability is proposed in this paper. The fixed platform of the hybrid manipulator connects the moving platform by two identical actuated (PRR)2RH kinematic chains. The full rotational capability is achieved by using two coaxial helical (H) joints with equal but opposite pitch connected to the moving platform. Mobility analysis, inverse and forward kinematics, singularity analysis and workspace of this manipulator are presented. Based on a homogenized Jacobian matrix, condition number and global dexterity index are used to evaluate the kinematic performance of the 2-(PRR)2RH hybrid manipulator. The connection among the workspace volume, the global dexterity index and the layout angle of the manipulator are disclosed. The parameter-finiteness normalization method is then used to produce an optimal design of link parameters. The results provide theoretical foundations for application of this novel manipulator.

Classification of 3T1R Parallel Manipulators Based on Their Wrench Graph

This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.

Elastodynamic optimization of a 3T1R parallel manipulator

In this paper the elastodynamic optimization of a 3T1R parallel manipulator is performed. The robot is first divided into subsystems including its four legs and the moving platform; then, each leg is split into three modules. A module is made of flexible and rigid links coupled by means of ideal joints. Once the global stiffness and inertia matrices are obtained upon assembling all modules of the subsystems, two constrained optimization techniques are first employed: the fixed pose optimization and the global optimization inside a cube. The multi-objective function is focused on the first natural frequency and its distribution within the robot's constant orientation workspace. Such an optimization combines two conflicting criteria: the need to have a stiff manipulator and the requirement to have a lightweight structure. The optimization variables pertain to only geometric parameters, while considering all materials and structural parameters as defined. Equality and inequality constraints are also included limiting the total mass of the robot, links' lengths and cross section diameters. In order to avoid workspace's volume reduction, a third optimization, based on diameter resizing, is finally described.

Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures

Abstract This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction (3T1R). Eleven architectures obtained from a recent type synthesis of such manipulators are analyzed. The constraint analysis shows that these architectures are all overconstrained and share some common properties between the actuation and the constraint wrenches. The singularities of such manipulators are examined through the singularity analysis of the 4-RUU parallel manipulator. A wrench graph representing the constraint wrenches and the actuation forces of the manipulator is introduced to formulate its superbracket. Grassmann–Cayley Algebra is used to obtain geometric singularity conditions. Based on the concept of wrench graph, Grassmann geometry is used to show the rank deficiency of the Jacobian matrix for the singularity conditions. Finally, this paper shows the general aspect of the obtained singularity conditions and their validity for 3T1R parallel manipulators with identical limb structures.

Forward displacement analysis of a quadratic 4-DOF 3T1R parallel manipulator

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) and the Type II singularity analysis of a quadratic 4-DOF 3T1R (SCARA) parallel manipulator: the Quadrupteron. It will be proved that there exists a one-to-one correspondence between the two formulas, each producing one solution to the FDA, and the two singularity-free regions. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-free region in which it works is specified. The Type II singularity analysis in the joint space will also be investigated in order to identify the conditions on the inputs to keep the Quadrupteron working in the same singularity-free region in its Cartesian workspace.

Design and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator With High-Load Carrying Capacity

In this paper, a new four degrees of freedom 3T1R parallel manipulator with high-load carrying capacity is presented. This manipulator generates Schönflies motions, in which the moving platform carries out three independent translations and one rotation about one axis of fixed orientation. The particularity of the proposed architecture is the decoupling of the displacements of the platform in the horizontal plane from the platform’s translation along the vertical axis. Such a decoupling allows the cancellation of the gravity loads on the actuators, which displace the platform in the horizontal plane. A prototype of the proposed manipulator with four degrees of freedom and an experimental validation of the suggested concept are also presented. Two cases have been examined on the built prototype: a manipulator with payload and one without. It was shown that the input torques of actuators displacing the platform in the horizontal plane for these two cases are the same; i.e., the payload does not bring any load to the actuators.

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schönflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations, and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.