Constant Orientation Workspace Research Articles

Design and analysis of a novel 3-DOF planar parallel manipulator with two kinematic chains

In this work, to enlarge the workspace, a novel 3-DOF planar parallel manipulator (PPM) with two identical RRR kinematic chains is proposed, and this manipulator has a significant advantage in orienting the moving platform (MP) across a wide range of angles. Resorting to the closed-loop vector approach, the inverse position equation and Jacobian matrix of the novel manipulator are established. Payload performance, dexterity performance, and singularity of the proposed manipulator are analyzed based on the Jacobian matrix. To investigate the distribution characteristics of the constant orientation workspace, orientation workspace, and reachable workspace of the proposed manipulator, a numerical discretization method is employed. Under the same working mode and structural parameters, constant orientation workspace and reachable workspace comparisons between the proposed manipulator and another two traditional PPMs are conducted. Focused on three kinds of performance indices, link lengths optimization of the proposed manipulator is carried out. A 4-DOF pick-and-place equipment is fabricated, and the rotational and translational capabilities are verified based on two examples.

Methods of workspace generation for parallel kinematic manipulators

This paper presents the geometric, discretization and Monte Carlo method to generate the workspace for Parallel Kinematic Manipulators (PKMs). The geometric method does not require the solution to the inverse kinematics as opposed to the Monte Carlo and discretization methods. Each method possesses advantages and drawbacks concerning accuracy, time and ease of implementation. A case study concerning constant orientation workspace of a planar 3RRR PKM showed that the most efficient and accurate method was the geometric method but it also possessed the most limitations. The discretization and Monte Carlo methods produced the workspace with an accuracy of 92.49% and 95.67% respectively.

Workspace and performance analysis of a 6-DOF hexapod-type manipulator with a circular guide

The present paper considers workspace and performance analysis of a six degree-of-freedom hexapod-type parallel manipulator with a circular guide. Compared to other similar manipulators, the design of this one allows locating all the drives fixed on the base and avoiding collisions between the carriages. The first half of the paper focuses on a procedure to determine the constant orientation (translation) workspace. The study first considers all the constraints that can affect the working area: constraints in active and passive joints, leg interference, and singularities. Next, the paper discusses the numerical procedure to construct the workspace. The proposed innovative approach combines the features of conventional geometrical and discretization methods. The suggested techniques are implemented in a MATLAB package and verified by examples with various orientations of the mechanism output link. The paper also discusses the accuracy of developed methods and mentions the required computational efforts. The second half of the work analyzes manipulator performance by calculating the conditioning index over the workspaces obtained earlier. The paper evaluates the conditioning index for an ordinary Jacobian matrix and a normalized one. In the latter case, two normalization approaches are considered: using a characteristic length and using linear velocities of three points selected on the mechanism output link.

Workspace Computation of Planar Continuum Parallel Robots

Continuum parallel robots ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CPRs</i> ) comprise several flexible beams connected in parallel to an end-effector. They combine the inherent compliance of continuum robots with the high payload capacity of parallel robots. Workspace characterization is a crucial point in the performance evaluation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CPRs</i> . In this paper, we propose a methodology for the workspace evaluation of planar continuum parallel robots ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PCPRs</i> ), with focus on the constant-orientation workspace. An explorative algorithm, based on the iterative solution of the inverse geometrico-static problem is proposed for the workspace computation of a generic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PCPR</i> . Thanks to an energy-based modelling strategy, and derivative approximation by finite differences, we are able to apply the Kantorovich theorem to certify the existence, uniqueness, and convergence of the solution of the inverse geometrico-static problem at each step of the procedure. Three case studies are shown to demonstrate the effectiveness of the proposed approach.

Algorithm to Determine the Volume and Shape of Constant Orientation Workspace for a 2(3-RRPS) Parallel Robot

This article describes a geometrical method used to analyze the workspace for parallel robot 2(3-RRPS). The algorithm, implemented in a CAD software, determines the workspace for a constant orientation. Mechanical restrictions of the robot and its influence in the workspace are considered. Actuator stroke, angular stroke of the joints in the base, angular travel of the ball joints on the platform, closing restriction and chain interference are the restrictions considered. Applications of the method are presented, such as the characterization of the workspace, the graphic obtaining of it for a range of orientations and the analysis of the effect that the joint limits have on it. Determination of the workspace for orientations range, shape parameters, quantification of the effect of a restriction on the volume, synthesis and dimensional optimization of the mechanism are examples presented to show the potentiality of the algorithm.

Inverse dynamics and trajectory tracking control of a new six degrees of freedom spatial 3-RPRS parallel manipulator

Abstract. This paper presents the complete dynamic model of a new six degrees of freedom (DOF) spatial 3-RPRS parallel manipulator. The geometry parameters of the manipulator are optimized for a given constant orientation workspace. Further, a robust task-space trajectory tracking control is also designed for the manipulator along with a nonlinear disturbance observer. To demonstrate the efficacy and show the complete performance of the proposed controller, virtual prototype experiments are executed using one of the multibody dynamics software namely MSC Adams. The computer-based virtual prototype experiment results show that the manipulator tracking performance is satisfactory with the proposed control scheme. In addition, the controller parameter sensitivity and robustness analyses are also accomplished.

A novel numerical approach for workspace determination of parallel mechanisms

In this paper, a novel numerical approach is proposed for workspace determination of parallel mechanisms. Compared with the classical numerical approaches, this presented approach discretizes both location and orientation of the mechanism simultaneously, not only one of the two. This technique makes the presented numerical approach applicable in determining almost all types of workspaces, while traditional numerical approaches are only applicable in determining the constant orientation workspace and orientation workspace. The presented approach and its steps to determine the inclusive orientation workspace and total orientation workspace are described in detail. A lower-mobility parallel mechanism and a six-degrees-of-freedom Stewart platform are set as examples, the workspaces of these mechanisms are estimated and visualized by the proposed numerical approach. Furthermore, the efficiency of the presented approach is discussed. The examples show that the presented approach is applicable in determining the inclusive orientation workspace and total orientation workspace of parallel mechanisms with high efficiency.

Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators

SUMMARYOptimization is an important step in the design and development of a planar parallel manipulator. For optimization processes, workspace analysis is a crucial and preliminary objective. Generally, the workspace analysis for such manipulators is carried out using a non-dimensional approach. For planar parallel manipulators of two degrees of freedom (2-DOF), a non-dimensional workspace analysis is very advantageous. However, it becomes very difficult in the case of 3-DOF and higher DOF manipulators because of the complex shape of the workspace. In this study, the workspace shape is classified as a function of the geometric parameters, and the closed-form area expressions are derived for a constant orientation workspace of a three revolute–revolute–revolute (3-RRR) planar manipulator. The approach is also shown to be feasible for different orientations of a mobile platform. An optimization procedure for the design of planar 3-RRR manipulators is proposed for a prescribed workspace area. It is observed that the closed-form area expression for all the possible shapes of the workspace provides a larger solution space, which is further optimized considering singularity, mass of the manipulator, and a force transmission index.

Determination of Constant Orientation Workspace of a Stewart Platform by Geometrical Method

Determination of workspace is one of the main considerations in the design of any robot since the workspace geometry is considered a fundamental issue for robot design. This also plays a crucial role in trajectory planning. Among parallel manipulators, 6-DOF Stewart platforms is the most researched and widely used robot. However, till date there is no closed form expression of workspace volume for Stewart platform. In this paper, a novel method is proposed to find out the workspace volume of Stewart platform. In this paper, individual workspace of each leg of the manipulator (P-U-S) is determined and then translated by a common distance towards their geometrical center thus generating constant orientation workspace. To determine the workspace volume, geometric intersection of the six spheres is computed. This results in workspace of definite shape and size, whose volume is calculated using simple formulae. It is observed that the geometric way of determination of workspace area is computationally less tedious than the algebraic method. This also helps a lot for workspace optimization of such manipulators.

Design and Analysis of 3R2T and 3R3T Parallel Mechanisms With High Rotational Capability

This paper describes the design, kinematics, and workspace analysis of 3R2T and 3R3T parallel mechanisms (PMs) with large rotational angles about three axes. Since the design of PMs with high rotational capability is still a challenge, we propose the use of a new nonrigid (or articulated) moving platform with passive joints in order to reduce the interference between limbs and the moving platform. According to the proposed nonrigid platform and Lie subgroup of displacement theory, several 3R2T and 3R3T PMs are presented. Subsequently, the inverse kinematics and velocity analysis of one of the proposed mechanisms are detailed. Based on the derived inverse kinematic model, the constant-orientation workspace is computed numerically. Then, the analysis of rotational capability about the three axes is performed. The result shows that even if interference and singularity are taken into account, the proposed mechanisms still reveal the high continuously rotational capability about the three axes, by means of actuation redundancy.

Determining the maximal singularity-free circle or sphere of parallel mechanisms using interval analysis

SUMMARYThis paper proposes a systematic algorithm based on the concept of interval analysis to obtain the maximal singularity-free circle or sphere within the workspace of parallel mechanisms. As case studies the 3-RPR planar and 6-UPS parallel mechanisms are considered to illustrate the relevance of the algorithm for 2D and 3D workspaces. To this end, the main algorithm is divided into four sub-algorithms, which eases the understanding of the main approach and leads to a more effective and robust algorithm to solve the problem. The first step is introduced to obtain the constant-orientation workspace and then the singularity locus. The main purpose is to obtain the maximal singularity-free workspace for an initial guess. Eventually, the general maximal singularity-free workspace is obtained. The main contribution of the paper is the proposition of a systematic algorithm to obtain the maximal singularity-free circle/sphere in the workspace of parallel mechanisms. The combination of a maximal singularity-free circle or sphere with the workspace analysis by taking into account the stroke of actuators, as additional constraint to the latter problem, is considered. Moreover, the center point of the circle/sphere is not restrained to a prescribed point.

SHeRo: Scalable hexapod robot for maintenance, repair, and operations

Abstract Improper maintenance, repair, and operations of societal centric structures can lead to catastrophic failures that drastically affect global economy, the environment, and everyday life. Due to the remote, cramped and highly irregular environmental nature of these structures, routine manual procedures and operations can be rather tedious, dangerous, and hazardous for humans. Automating maintenance, repair, and operations removes human workers from having to crawl within highly cluttered and constrained spaces, breathing in stale air mixed with fumes from welding or particulate from repair work, and provides higher reliability and consistency in the repair work. This paper introduces SHeRo, a scalable hexapod robot designed for maintenance, repair, and operations within remote, inaccessible, irregular, and hazardous environments. The scalability of the design enhances traditional hexapod robot designs by incorporating two prismatic joints into each leg. A detailed discussion on the design and realization of SHeRo is provided. An analysis on the stability and workspace of SHeRo is presented and a dynamic criterion is developed to integrate the concepts of robot stability and constant orientation workspace into a stable workspace. The analytical solution of the lateral stable workspace of SHeRo is derived along with a metric for comparing stable workspace between different robot configurations. A simulated demonstration and two physical experimental demonstrations are presented showing the advantage of introducing scalability into the hexapod robot design along with the workspace enhancement and flexibility of the scalable hexapod robot.

Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots

The workspace of hexapod robots is a key performance parameter which has attracted the attention of numerous researchers during the past decades. The selection of the hexapod parameters for a desired workspace generally employs the use of numerical methods. This paper presents a general methodology for solving the closed-form constant orientation workspace of radially symmetric hexapod robots. The closed-form solution facilitates hexapod robot design and minimizes numerical efforts with on-line determination of stability and workspace utilization. The methodology can be used for robots with nonsymmetric and nonidentical kinematic chains. In this paper, the methodology is used to derive the closed-form equations of the boundary of the constant-orientation workspace of axially symmetric hexapod robots. Several applications are provided to demonstrate the capability of the presented closed-form solution in design and optimization. An approach for workspace-based design optimization is presented using the provided analytical solution by applying an iterative optimization algorithm to the find optimized structural parameters and an optimized workspace.

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.

A 6-DOF reconfigurable hybrid parallel manipulator

This paper presents a case study on a reconfigurable hybrid parallel robot dubbed ReSl-Bot. It addresses the realm of reconfigurable 6-DOF parallel mechanisms, for sustainable manufacturing. It also features a self-reconfigurable architecture. A systematic analysis involving kinematics, constant orientation workspace, singularity and stiffness is developed in detail. Interesting features are discussed, revealing some unique characteristics of the studied architecture. A multi-objective optimization procedure is also carried out with weighted stiffness, dexterity and workspace volume as the performance indices.

A Fast Search Method for Computing the Constant-Orientation Workspace Based on the Binary Approximating Principle

In order to compute the constant-orientation workspace of serial robots, a fast search method based on the binary approximating principle is proposed. On the basis of binary tests of the inverse kinematics and the collision detection of a robot, this method introduces virtual straight lines containing the orientation information and selects two points(one locates inside the constant-orientation workspace, while the other outside) to carry out the dichotomy and test processes, so as to approach the boundary of the constant-orientation workspace step by step. Firstly, the concept and the state of the art of constant-orientation workspace are introduced in brief. The constant-orientation workspace problem is abstracted, followed by the basic solving ideas. Then the binary approximating search method and its applications to computing the 1D、2D and 3D constant-orientation workspace are presented in detail. Finally, the effectiveness of the proposed method is demonstrated by simulations and comparisons, showing that the method achieves the accuracy as 1 mm consuming about 14.5 ms to search the 1D constant-orientation workspace, and is suitable for solving the 1D ~ 3D collision-free constant-orientation workspace problem of robots with different degrees of freedom or configurations.

Simulation of a 6-PUS jaw robot and a new mechanism inspired by masticatory system

A jaw robot based on the 6-PUS parallel mechanism was introduced according to the biomechanical properties of mandibular muscles. For a given mandibular trajectory to be tracked, the inverse kinematics solution is derived and Jacobian matrix formulated from differential kinematics is found. Kinematics performances, such as constant orientation workspace and manipulability are simulated via numerical method. These indices show that the parallel mechanism has enough flexible workspace without singularity, and has a good motion transmission performance for human chewing movement. In order to reproduce jaw motions and mechanics that match the human jaw function truthfully with the conception of bionics, the temporomandibular joints (TMJs) are taken into account. Another novel actuation redundant mechanism for the jaw robot is proposed based on mechanical biomimetic principles, which has four degrees of freedom, but is driven by six actuators.

Design of mechanical coxa joints based on three-degree-of-freedom spherical parallel manipulators

We addressed the issue of the design of mechanical coxa joints based on three-degree-of-freedom spherical parallel manipulators using the parameter statistics optimum method based on index atlases. The coxa joints have the advantages of high payload, high accuracy, and good technological efficiency. The first step of the design and prototyping used in this paper develops the direct and inverse displacement equations from the layout feature of the mechanical coxa joints. Then, the shapes of a constant-orientation workspace of the mechanical coxa joints are described, and the effects of the design parameters on the workspace volume are studied quantitatively. The next step deals with the graphical representation of the atlases that illustrates the relationship between performance evaluation index and design parameters based on the kinematics and torque analysis of the mechanical coxa joints. Finally, the geometric parameters of the coxa joints are obtained by the parameter statistics optimum method based on the index atlases. Considering assembly conditions, the design scheme of the mechanical coxa joints is developed, which provides a theoretical basis for the application of the mechanical coxa joints.

Design and Analysis of Cooperative Cable Parallel Manipulators for Multiple Mobile Cranes

The design, dynamic modelling, and workspace are presented in this paper concerning cooperative cable parallel manipulators for multiple mobile cranes (CPMMCs). The CPMMCs can handle complex tasks that are more difficult or even impossible for a single mobile crane. Kinematics and dynamics of the CPMMCs are studied on the basis of geometric methodology and d'Alembert's principle, and a mathematical model of the CPMMCs is developed and presented with dynamic simulation. The constant orientation workspace analysis of the CPMMCs is carried out additionally. As an example, a cooperative cable parallel manipulator for triple mobile cranes with 6 Degrees of Freedom is investigated on the basis of the above design objectives.

Mobility and kinematic analysis of a parallel mechanism with both PPR and planar operation modes

This paper proposes a 1-RPU-2-UPU parallel manipulator with both PPR and planar operation modes. The mobility of the moving platform of the parallel manipulator in the two operational modes is analyzed via screw theory. The parallel manipulator has 3 degrees-of-freedom and allows the moving platform to move along a plane in the planar operation mode and to rotate about an axis that translates along a plane in the PPR operation mode. The transition between the two operational modes through transitional configurations is also discussed. The inverse and forward kinematic analysis and singularity analysis of the parallel manipulator are then dealt with by a vector approach. Finally, the constant orientation workspace and the reachable workspace are presented for the parallel manipulator in both operation modes.