Workspace Volume Research Articles

Interactions and Optimizations Analysis between Stiffness and Workspace of 3-UPU Robotic Mechanism

Abstract The interactions between stiffness and workspace performances are studied. The stiffness in x, y and z directions as well as the workspace of a 3-UPU mechanism are studied and optimized. The stiffness of the robotic system in every single moveable direction is measured and analyzed, and it is observed that in the case where one tries to make the x and y translational stiffness larger, the z directional stiffness will be reduced, i.e. the x and y translational stiffness contradicts with the one in z direction. Subsequently, the objective functions for the summation of the x and y translational stiffness and z directional stiffness are established and they are being optimized simultaneously. However, we later found that these two objectives are not in the same scale; a normalization of the objectives is thus taken into consideration. Meanwhile, the robotic system’s workspace is studied and optimized. Through comparing the stiffness landscape and the workspace volume landscape, it is also observed that the z translational stiffness shows the same changing tendency with the workspace volume’s changing tendency while the x and y translational stiffness shows the opposite changing tendency compared to the workspace volume’s. Via employing the Pareto front theory and differential evolution, the summation of the x and y translational stiffness and the volume of the workspace are being simultaneously optimized. Finally, the mechanism is employed to synthesize an exercise-walking machine for stroke patients.

Stiffness modeling and optimization of a 3-DOF parallel robot in a serial-parallel polishing machine

Polishing is a kind of finishing process that can effectively reduce the surface defects and improve the form accuracy. This paper presents a novel hybrid machine with 6 degrees of freedom (DOF) serial-parallel topological structure used as an ultra-precision polishing equipment which is composed of a 3-DOF parallel robot, a 2-DOF serial robot and a turntable providing a redundant DOF. Due to the complexity of structure, stiffness performance evaluation of the parallel robot becomes a challenge. As a result, a theoretical model of the parallel robot based on the virtual work principle and the deformation superposition principle is formulated for analyzing the stiffness performance. With the developed model, a multi-objective dimensional optimization method is developed to maximize both the workspace volume and the global stiffness performance of the parallel robot. Artificial intelligence approach based on genetic algorithms is implemented to obtain an optimal combination of structural parameters. The effectiveness of this method is validated by simulation and the parallel robot with optimized structural parameters has a workspace with higher stiffness performance, hence justifies its suitability for high precision polishing.

Optimizing Stiffness and Dexterity of Planar Adaptive Cable-Driven Parallel Robots

Adaptive cable-driven parallel robots are a special subclass of cable-driven systems in which the locations of the pulley blocks are modified as a function of the end-effector pose to obtain optimal values of given performance indices within a target workspace. Due to their augmented kinematic redundancy, such systems enable larger workspace volume and higher performance compared to traditional designs featuring the same number of cables. Previous studies have introduced a systematic method to optimize design and trajectory planning of the moving pulley-blocks for a given performance index. In this paper, we study the motions of the pulley blocks that optimize two performance indices simultaneously: stiffness and dexterity. Specifically, we present a method to determine the pulley blocks motions that guarantee ideal dexterity with the best feasible elastic stiffness, as well as those that guarantee isotropic elastic stiffness with the best feasible dexterity. We demonstrate the proposed approach on some practical cases of planar adaptive cable-driven parallel robots.

OPTIMAL DESIGN PARAMETERS OF RECONFIGURABLE ROBOTS WITH LOCKABLE JOINTS

This paper presents a global optimization methodology to find the optimal Denavit–Hartenberg parameters of a serial reconfigurable manipulator minimizing a cost function over a pre-specified workspace volume and given lower and upper bounds on the design parameters. Different cost functions such as the manipulability measure, maximum force capability of the manipulator’s end-effector, and maximum velocity capability of the manipulator within the operating workspace of the manipulator are considered to optimize the kinematic design. Based on a combination of genetic algorithm (GA) and sequential quadratic programming (SQP), a modified global and posture-independent parameter of singularity (MPIPS) is presented. Finally, a weighted objective function is proposed to balance between the conflicting requirements for manipulator’s force and velocity capabilities.

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.

Design of an anthropomorphic dual-arm robot with biologically inspired 8-DOF arms

From the perspective of kinematics, dual-arm manipulation in robots differs from single-arm manipulation in that it requires high dexterity in a specific region of the manipulator's workspace. This feature has motivated research on the specialized design of manipulators for dual-arm robots. These recently introduced robots often utilize a shoulder structure with a tilted angle of some magnitude. The tilted shoulder yields better kinematic performance for dual-arm manipulation, such as a wider common workspace for each arm. However, this method tends to reduce total workspace volume, which results in lower kinematic performance for single-arm tasks in the outer region of the workspace. To overcome this trade-off, the authors of this study propose a design for a dual-arm robot with a biologically inspired four degree-of-freedom shoulder mechanism. This study analyzes the kinematic performance of the proposed design and compares it with that of a conventional dual-arm robot from the perspective of workspace and single-/dual-arm manipulability. The comparative analysis revealed that the proposed structure can significantly enhance single- and dual-arm kinematic performance in comparison with conventional dual-arm structures. This superior kinematic performance was verified through experiments, which showed that the proposed method required shorter settling time and trajectory-following performance than the conventional dual-arm robot.

Determining workspace parameters for a new type of 6RSS parallel manipulator based on structural and geometric models

Workspace geometric modelling of a new type of 6RSS parallel manipulator is described below. In the beginning, the researches undertaken in this area by other authors are highlighted and then a definition of this type of mechanisms is provided. The structural model of the 6RSS manipulator is briefly described. Inverse geometric model and translation subspace methods are used in order to determine the dimensions that define the workspace volume of the parallel manipulator. The reachable workspace is defined as a subset of the whole workspace in relation with the positions achieved by the characteristic point.

PARAMETRIC DESIGN OF DELTA ROBOT

This article describes a sophisticated determination and presentation of a workspace volume for a delta robot, with consideration of its kinematic behavior. With the help of theoretical equations, optimization is performed with the aid of the stiffness and dexterity analysis. Theoretical substructure is coded in Matlab and three-dimensional (3D) data for delta robot are developed in computer-aided design (CAD) environment. In later stages of the project, both 3D and theoretical data are linked together and thus, with the changing design parameter of the robot itself, the Solidworks CAD output adapts and regenerates output with a new set of parameters. To achieve an optimum workspace volume with predefined parameters, a different set of robot parameters are iterated through design optimization in Matlab, and the delta robot design is finalized and illustrated in the 3D CAD environment, Solidworks. This study provides a technical solution to accomplish a generic delta robot with optimized workspace volume.

Path planning and assembly mode-changes of 6-DOF Stewart-Gough-type parallel manipulators

The Stewart-Gough platform (SGP) is a six degree-of-freedom (DOF) parallel manipulator whose reachable workspace is complex due to its closed-loop configuration and six DOF outputs. As such, methods of path planning that involve storing the entire reachable workspace in memory at high resolutions are not feasible due to this six-dimensional workspace. In addition, complete path planning algorithms struggle in higher dimensional applications without significant customisations. As a result, many workspace analysis algorithms and path planning schemes use iterative techniques, particularly when tracking the manipulator's many direct kinematic solutions. The aim of this paper is to present the viability of singularity-free path planning in the Stewart-Gough platform's 6-dimensional workspace on modern-day computing systems by demonstrating its assembly mode-changing capability. The entire workspace volume is found using flood-fill algorithms with smooth and singularity-free trajectories generated within this known workspace. Workspace volume analysis was also performed with results comparable to other works.

Design optimization of 3PRS parallel manipulator using global performance indices

This paper presents an optimal kinetostatic design method for a general 3PRS (Prismatic-revolute-spherical) spatial parallel manipulator by formulating a multi-objective optimization problem considering the performance indices are as the objective functions. Three performance criteria—Global conditioning index (GCI), Global stiffness index (GSI) and workspace volume-were formulated and the effect of actuator layout angle on the performance indices was studied. A multi-objective evolutionary algorithm based on the Control elitist non-dominated sorting genetic algorithm (CENSGA) was adopted to find the final approximation set. The optimal geometric parameters that yield minimal compliance with larger workspace volume and improved dexterity are suggested for a general 3PRS parallel manipulator. For the optimal design, it is shown that global isotropy and global stiffness of the platform is improved at the cost of workspace reduction.

Validity and reliability of two protocols for measuring Reachable Workspace Volume in able-bodied and stroke subjects.

Researchers are measuring Reachable Workspace Volume (RWV) to assess the effects of various interventions on impaired upper extremity function. These measurement protocols have not been validated. Assess the validity and reliability of two RWV protocols. Fifteen able-bodied subjects and eight stroke subjects participated. Two RWV protocols (POLES and PLANES) were completed and compared with hemi-spheric volume estimations using the average reach in the Modified Functional Reach Test (MFRT). RWV, based on the movement of a single hand marker, was calculated using a 3D motion analysis system (Vicon, Centennial, CO, USA). Intraclass correlation coefficients (ICC) represented reliability, Pearson's linear correlation coefficient (r) between RWVs and MFRT represented validity, and p < 0.05 represented significant differences between the volumes. For the able-bodied subjects, the POLES protocol had excellent validity and excellent reliability, the PLANES protocol had good validity and excellent reliability, and both RWVs were significantly larger than estimated MFRT volume. In the stroke subjects, both protocols had good validity, excellent reliability, and RWVs which were significantly smaller than the estimated MFRT volume. Both measurement protocols provided valid and reliable measures of RWV. MFRT may underestimate RWV in able-bodied subjects, and overestimate RWV in stroke subjects.

The design of a new remote manipulator for space operation using a 4-cable-driven thrusters-embedded configuration

A new remote manipulator based on cable-driven parallel mechanism (CDPM) is designed for space long-distance operations (e.g. space capture/docking and other long-distance space activities) in this paper. By controlling the cables and thrusters which are equipped on the manipulator simultaneously, the new remote manipulator can achieve expected position, linear velocity, and angular velocity. The new manipulator has a larger controllable workspace compared with usual CDPMs. The structure and characteristics of this manipulator are discussed in this paper. The volume and characteristics of the workspace are also discussed. The influence of the distance on the static equilibrium is studied. The simulation results show that the workspace of this new manipulator is larger than usual CDPM's. The results also indicate that the cable forces and thruster vectors can completely constrain the manipulator and meet the requirements of space activities. The results of the simulation also show that the controllable workspace of the manipulator is not continuous at some regions. Hence, trajectory planning is necessary.

Optimal design of a 3-leg 6-DOF parallel manipulator for a specific workspace

Researchers seldom study optimum design of a six-degree-of-freedom(DOF) parallel manipulator with three legs based upon the given workspace. An optimal design method of a novel three-leg six-DOF parallel manipulator(TLPM) is presented. The mechanical structure of this robot is introduced, with this structure the kinematic constrain equations is decoupled. Analytical solutions of the forward kinematics are worked out, one configuration of this robot, including position and orientation of the end-effector are graphically displayed. Then, on the basis of several extreme positions of the kinematic performances, the task workspace is given. An algorithm of optimal designing is introduced to find the smallest dimensional parameters of the proposed robot. Examples illustrate the design results, and a design stability index is introduced, which ensures that the robot remains a safe distance from the boundary of sits actual workspace. Finally, one prototype of the robot is developed based on this method. This method can easily find appropriate kinematic parameters that can size a robot having the smallest workspace enclosing a predefined task workspace. It improves the design efficiency, ensures that the robot has a small mechanical size possesses a large given workspace volume, and meets the lightweight design requirements.

Kinematic Analysis of a 3-dof Parallel Machine Tool with Large Workspace

Kinematics of a 3-dof (degree of freedom) parallel machine tool with large workspace was analyzed. The workspace volume and surface and boundary posture angles of the 3-dof parallel machine tool are relatively large. Firstly, three dimensional simulation manipulator of the 3-dof parallel machine tool was constructed, and its joint distribution was described. Secondly, kinematic models of the 3-dof parallel machine tool were fixed on, including displacement analysis, velocity analysis, and acceleration analysis. Finally, the kinematic models of the machine tool were verified by a numerical example. The study result has an important significance to the application of the parallel machine tool.

Designing a Novel Three-Degree-of-Freedom Parallel Robot Based on Workspace

This paper presents a novel three-degree-of-freedom (3-DOF) parallel manipulator and introduces its mechanical structure. Analytical solutions of the forward kinematics have been worked out, and all configurations of this robot are graphically displayed. On the basis of several special positions in the kinematics, a task workspace is prescribed to find the smallest feasible dimensional parameters of the robot. An algorithm describing this method is also introduced. This method can easily find appropriate parameters that can size a robot having the smallest workspace enclosing a predefined task workspace. This improves the design efficiency and ensures that the robot has a small mechanical size possessing a large workspace volume and, in terms of dimension design, meets the lightweight-design requirements. With examples illustrating the design results, we further introduce a design stability in dextoensure that the robot remains a safe distance from the boundary of its actual workspace. One prototype of the robot has already been developed.

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.

Kinematic Analysis and Dimensional Synthesis of Exechon Parallel Kinematic Machine for Large Volume Machining

A parallel kinematic machine (PKM) topology can only give its best performance when its geometrical parameters are optimized. In this paper, dimensional synthesis of a newly developed PKM is presented for the first time. An optimization method is developed with the objective to maximize both workspace volume and global dexterity of the PKM. Results show that the method can effectively identify design parameter changes under different weighted objectives. The PKM with optimized dimensions has a large workspace to footprint ratio and a large well-conditioned workspace, hence justifies its suitability for large volume machining.

Validity and Reliability of Two Reachable Workspace Volume Protocols in Able-Bodied and Stroke Subjects

Validity and Reliability of Two Reachable Workspace Volume Protocols in Able-Bodied and Stroke Subjects

Comparative Analysis of a Redundant Pentapod Parallel Kinematic Machine

Parallel kinematic mechanisms (PKMs) provide high stiffness and compact structures that are suitable for a large number of applications, including 5-axis milling. This paper presents a new pentapod-based PKM with an additional redundant degree-of-freedom (DOF) capable of reaching platform tilt angles of at least 90 deg over a large workspace. The proposed new PKM has a 6DOF 4 × SPRR + 1 × PSPR architecture. It is compared herein to Metrom® Pentapod as well as to several other pertinent PKMs in terms of workspace and dynamic stiffness. It is shown that the proposed mechanism can yield a tangibly larger workspace volume, when compared to those PKMs, while maintaining its high stiffness characteristics.

Optimization of a crossbar parallel machine tool based on workspace and dexterity

Increasing workspace and improving dexterity are important tasks for the design of parallel machine tools. The workspace of a crossbar parallel machine tool with constraints is obtained by using a 3D search method based on inverse kinematics. The new Jacobian matrix of the machine is also derived by using the natural coordinate method. Dexterity distribution of the machine tool is obtained on the basis of the workspace and the new Jacobian matrix. Influences of the structural parameters on the workspace volume index (WVI) and global dexterity index (GDI) are analyzed. Structural optimization is conducted by treating the WVI and GDI as the global optimization goals. Unlike the initial data, the optimized results increased by 0.43 and 0.34 times.