Orientational Workspace Research Articles

Kinematically redundant (6＋2)-dof HEXA robot for singularity avoidance and workspace augmentation

This paper introduces a novel (6＋2)-degree-of-freedom (dof) kinematically redundant parallel robot. The proposed architecture is based on the 6-dof HEXA parallel robot. The paper applies methodologies for avoiding type II singularities using kinematic redundancy that were originally proposed for robots with prismatic actuators to a new architecture with revolute actuators. The singularities of the HEXA robot are first examined based on previous work, and new instances of singularities are discovered. The singularity locus in the orientational workspace is identified using the Power Inspired Measure. Then, a novel kinematically redundant leg architecture is proposed to allow for the avoidance of these type II singularities. It is shown that the singularities present within the orientational workspace can successfully be avoided if two kinematically redundant legs are included in the robot architecture. The performance of the new architecture is then examined in various trajectories within the orientational workspace. Results show that the attainable orientational workspace is significantly increased with the proposed architecture.

Exploiting the Kinematic Redundancy of a (6 + 3)-Degree-of-Freedom Parallel Manipulator to Produce Unlimited Rotation of the Platform

Abstract Mechanical interference and singularities within the reachable workspace often restrict the orientational workspace of parallel robots. Introducing kinematic redundancy can alleviate this limitation. This paper discusses the possibility to produce unlimited rotation of the platform of a tripedal (6 + 3)-degree-of-freedom kinematically redundant parallel robot. The articulated platform of such a robot has three degrees of mobility. The platforms considered here are planar linkages that contain either revolute or prismatic joints. It is shown that at least two revolute joints are required to produce unlimited rotation with appropriate design and initial configuration, while the platforms with two prismatic joints cannot produce such rotations without crossing a singularity.

Multi-Objective Optimization of 1T2R Parallel Mechanisms Without Fixed Orientation Center and Axis Under the Influence of Parameter Perturbation

To track moving targets and signals in space, multiple characteristics as large orientational workspace and excellent kinematic performance are required for the satellite antenna driving mechanism. Due to variable orientational center and axes, the 3-RSR mechanism is capable of 1T2R with continuous workspace and becomes a promising solution for the satellite antenna driving mechanism. Influenced by the topological structure characteristics as none fixed orientation center and axes, the performances of 3-RSR mechanism are significantly impacted by the parameter perturbation. According to the differential mapping between finite screw and instantaneous screw, the structure, kinematics, performance, and optimization are unified under the FIS theory. To be applied for the satellite antenna driving mechanism, this paper carries out the multi-objective optimization of 3-RSR mechanism under the influence of parameter perturbation based on the FIS theory. Firstly, the orientational workspace is obtained by finite screw and the instantaneous motion description of the mechanism is derived through calculation principle of FIS theory. Secondly, the orientational workspace and kinematics indices of the mechanism are proposed towards the actual requirements of the satellite antenna driving, and the relationship with the parameters is established. The discrete operation becomes extremely complex owing to parameter perturbation, and the RSMs (response surface model) of indices without considering and considering parameter perturbation are modeled. The multi-objectives optimization of 3-RSR mechanism influenced by parameter perturbation is carried out and its Pareto frontier is obtained. Finally, a point preferred strategy is proposed and the optimum value of the parameter from Pareto frontier is selected.

Singularity analysis of a kinematically redundant (6+2)-DOF parallel mechanism for general configurations

Parallel mechanisms suffer from type II singularities which reduce their useful orientational workspace. Adding kinematic redundancy in parallel mechanisms enhances their orientational workspace by providing singularity avoidance capabilities. However, an increasing number of kinematically redundant degrees of freedom (DOFs) requires additional actuators and makes the redundancy resolution more complex. Moreover, examples in the literature exist where a minimal number of kinematically redundant DOFs was used to produce a singularity-free orientational workspace for planar mechanisms. In this work, the architecture of a kinematically redundant (6+2)-DOF parallel mechanism akin to the well-known Gough–Stewart platform is studied, and its singularity locus is derived. The results show that, while some singularities still remain in the useful workspace of the mechanism, they can be accurately localized with simple closed-form analytical expressions for trajectory planning purposes. Furthermore, the redundancy resolution may find itself easy to handle, since the avoidable singularities and mechanical interference can be mapped into the 2-D space of the redundant parameters. Finally, the proposed architecture is considered as a compromise between obtaining a singularity-free workspace and handling easily the redundancy resolution for the trajectory planning.

Singularity analysis of a kinematically redundant (6+2)-DOF parallel mechanism for zero-torsion configurations

The orientational workspace of parallel mechanisms is known to be restricted due to singular configurations of type II. Recently, a (6+3)-degree-of-freedom (DOF) kinematically redundant parallel mechanism was proposed based on the well-known Gough–Stewart platform. It was shown that, for the specific architecture proposed, a minimum of three redundant DOFs is necessary to guarantee the existence of a non-singular configuration for any pose of the platform. This work presents a different architecture with two redundant DOFs instead of three, and has for primary objective to derive the singularity locus for zero-torsion configurations. The results indicate that the mathematically possible singularities are outside of the reachable workspace, suggesting that for zero-torsion trajectories, two kinematically redundant DOFs are sufficient to greatly enhance the orientational workspace of the proposed architecture. An example path with large tilting angle is presented in a multimedia extension of the article in order to demonstrate the capability of the mechanism to reach such orientations without encountering inevitable singularities.

Kinematics of a 6-DOF parallel manipulator with two limbs actuated by spherical motion generators

Inspired by dual-arm-like manipulation, a novel 6-DOF parallel manipulator with two spherical-universal-revolute limbs is proposed. Compared with general 6-DOF parallel manipulators with six limbs, this new manipulator actuated by spherical motion generators has only two limbs, which brings advantages such as fewer active limbs for avoiding interference, larger reachable and orientational workspace for complex operating, more actuators integrated in active modules for decreasing installation errors and increasing compactness. In this paper, the kinematics of this novel parallel manipulator is solved and illustrated, covering its inverse and forward position analysis, workspace and singularities. The kinematic study reveals interesting features of this manipulator such as multiple working and assembly modes, small footprint and large workspace volume with high dexterity. Numerical examples of kinematic analysis are included. Practical application of the new manipulator is illustrated.

A Backdrivable Kinematically Redundant (6+3)-Degree-of-Freedom Hybrid Parallel Robot for Intuitive Sensorless Physical Human–Robot Interaction

A novel backdrivable 3-[ <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> ( <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> R- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> RR)SR] kinematically redundant (6+3)-degree-of-freedom (DOF) spatial hybrid parallel robot with revolute actuators is proposed for low-impedance physical human–robot interaction. The kinematic model is developed based on the constraint conditions of the robot. It is shown that the type II (parallel) singularities can be completely avoided, thereby yielding a very large translational and orientational workspace. A workspace analysis is presented in order to demonstrate the capabilities of the robot. Mechanisms are then introduced to use the redundant DOF of the robot to operate a gripper with the robot actuators, which are mounted on or close to the base, thus reducing the inertia of the moving parts. The architecture of the robot makes it possible to use direct drive motors, thereby making the robot easily backdrivable and allowing the use of a very simple and effective controller. A prototype of the robot is then designed and built and the large workspace of the robot as well as the effortless physical human–robot interaction are demonstrated. The controller of the robot is then described, including a position control mode and a control mode for physical interaction, which does not require the use of a force/torque sensor or joint torque sensors. Because of its backdrivability and low moving inertia, the robot is particularly well-suited for physical human–robot interaction, as demonstrated in the accompanying videos.

Forward Kinematic Analysis of Kinematically Redundant Hybrid Parallel Robots

Abstract This paper focuses on the forward kinematic analysis of (6 + 3)-degree-of-freedom kinematically redundant hybrid parallel robots. Because all of the singularities are avoidable, the robot can cover a very large orientational workspace. The control of the robot requires the solution of the direct kinematic problem using the actuator encoder data as inputs. Seven different approaches of solving the forward kinematic problem based on different numbers of extra encoders are developed. It is revealed that five of these methods can produce a unique solution analytically or numerically. An example is given to validate the feasibility of these approaches. One of the provided approaches is applied to the real-time control of a prototype of the robot. It is also revealed that the proposed approaches can be applied to other kinematically redundant hybrid parallel robots proposed by the authors.

Singularity analysis and dexterity performance on a novel parallel mechanism with kinematic redundancy

This article presents a novel spatial parallel mechanism with kinematic redundancy. The design strategy and evolution of the proposed mechanism is introduced, and kinematic model of the mechanism is established. To simplify singularity analysis of this kind of mechanism, the virtual plane method which can separate the whole parallel mechanism into two parts is presented. The relative Jacobian matrices are established and illustrated with singularity configurations of three types. Kinematic performance is obtained to see redundancy effects on the mechanism. The orientational workspace is obtained by the regions of orientational angles with varied platform position. It shows the orientational workspace of the redundant mechanism is significantly larger. Evaluation of condition number demonstrates the proposed mechanism can clearly stay away from singularities with a large range of rotational angles. A trajectory example is conducted to further prove the proposed mechanism can produce a large range of rotational angles without meeting with singularities.

Kinematic Optimization of a Five Degrees-of-Freedom Spatial Parallel Mechanism With Large Orientational Workspace

This paper deals with the kinematic optimization of a five degrees-of-freedom (DoFs) spatial parallel mechanism with three kinematic chains. Inspired by the structure of the icosahedron, the base of the discussed mechanism has been designed into a compact and light-weight frame. Due to the potential advantages, this mechanism is used as a movable plug-in module in a multi-axis machine center to process large-scale parts with rotary contour surfaces. To derive its optimal parameters, kinematic optimization based on the motion/force transmissibility is carried out. The parameter design space (PDS) is generated first. Then, the performance evaluation index (i.e., local transmission index (LTI)) is derived sequentially. On this basis, the good transmission positioning workspace (GTPW) for a given orientation is defined by constraining the value of LTI with a certain metric. Thereafter, the atlases of the GTPW and the optimal region satisfying the workspace constraint are derived in the PDS. Within this region, a set of optimal parameters without dimension are selected. Consequently, the cuboid workspaces within GTPWs are identified in detail. By using the ratio between required workspace in application and the derived cuboid workspaces, optimal geometric parameters with dimension are derived. Workspace analysis results show that, for an arbitrary orientation between the vertical and horizontal directions, there is always a cuboid workspace within GTPW larger than required workspace. In addition, the orientational capability of the mechanism can reach more than 90 deg, and the flexible 2DoFs rotations can also be realized. The work in this paper is very helpful to the development of a mobile machining module.

Kinematically Redundant Spatial Parallel Mechanisms for Singularity Avoidance and Large Orientational Workspace

This paper introduces a novel architecture of kinematically redundant parallel mechanisms. This family of mechanisms is similar to the well-known Gough-Stewart platform, and it retains its advantages, i.e., the members connecting the base to the moving platform are only subjected to tensile/compressive loads. The proposed architecture exploits kinematic redundancy to avoid singularities and extend the rotational workspace. The novel kinematic architecture is described, and the associated kinematic relationships are developed. Based on the derivation of the Jacobian matrices, it is shown that the singularities of this type of mechanism are governed by the orientation of passive links connecting the redundant legs to the platform. Grassmann geometry is then used to demonstrate that, given some simple geometric assumptions on the architecture, all singularities can be avoided by exploiting the kinematic redundancy. The orientational workspace is then discussed, and a graphical representation is provided for an example architecture comprising nine actuators, whose orientational workspace is shown to be very large. The translational workspace is also studied. Example trajectories are given in order to illustrate the capabilities of the mechanism to produce very large rotation angles without encountering singularities. Computer animations of the trajectories are provided in a multimedia extension of the paper.

Design and analysis of a 6-DOF mobile parallel robot with 3 limbs

Mobile parallel robots (MPR), which structurally configured a moving platform and several parallel limbs with an actuating wheel at the end of each limb, exhibit advantages in high mobility, high load capability and high flexibility in complex task environments. In this paper, a 6-DOF MPR with 3-PPUU (Prismatic-Prismatic Universal-Universal) limbs is proposed. The structural scheme and inverse kinematics are first presented; the orientational workspace and the dexterity of the MPR are analyzed in detail. A parametric optimal design model is then developed; the optimal scheme of the MPR is obtained. The constant-posture control scheme and algorithm are also proposed in this paper. A prototype of the 3-PPUU MPR with omni-orientational wheels is developed and the precision for both translation and orientation of the prototype is measured by experiments, which verify the feasibility of the proposed MPR scheme.

Kinematics analysis of a novel parallel platform with passive constraint chain

A novel 4-DOF (degree of freedom) parallel platform with the passive constraint chain is proposed in this paper, according to the topology of the mechanism 4-UPS/1-RPU (4-Universal-Prismatic-Spherical joints and 1-Revolute-Prismatic-Universal joints). The inverse kinematics is studied in detail. In the formulation of Jacobian matrix of the presented parallel mechanism, the full Jacobian matrix with 6×6 dimensional matrix that consists of actuated Jacobian matrix and the constraint Jacobian matrix is formulated by the screw theory. The positional and orientational workspace is analysed using the method of boundary mapping. The dexterity analysis is then carried out based on the full Jacobian matrix under different orientations. As an application example of the proposed parallel mechanism a 5-DOF hybrid parallel kinematic machine is developed, verifying that the proposed novel parallel mechanism has the desired 4-DOFs and the dexterity of the mechanism is good enough to use in the machining process.

Workspace and singularity analysis of a double parallel manipulator

A double parallel manipulator (DPM) is composed of two parallel mechanisms with a central aids. The device is expected to have large workspace by reducing interference between links and to avoid singularity by constraining its motion. To prove this, workspace and singularity are analyzed. The workspace of the device is decoupled into a positional and an orientational workspace, each of which is computed and compared with that of a Stewart platform. The singularities occurring outside the workspace are analytically found at the configurations where a Jacobian matrix becomes rank deficient. To ascertain the analytical results, they are geometrically examined at the configurations where the duty for resisting forces and moments is not properly shared by a central axis and linear actuators due to losing static equilibrium. The geometrical results are coincident to the analytical results, which proves the DPM is free from the singularity problem.

Singularity analysis with respect to the workspace of a double parallel manipulator

Singularity analysis is an important issue in the design of parallel manipulators, since they become uncontrollable at singular configurations due to the rank deficiency of the Jacobian. This paper analyzes the singularity of a double parallel manipulator with respect to its workspace. The workspace is decoupled into a positional workspace generated by the first parallel mechanism, and an orientational workspace by the second mechanism. The singularities occurring outside each workspace are analytically found by a Jacobian matrix derived for the velocity transformation from the end-effecfor to the linear actuators. The singularity loci are presented and their geometric properties are examined to prove that the double parallel manipulator is free from the singularity problem.