Singular Configurations Research Articles

Design and performance analysis of a parallel wrist rehabilitation robot (PWRR)

Wrist rehabilitation robots are essential for assisting patients with stoke or wrist injuries. Such devices compensate for deficiencies in manual rehabilitation training, and reduce the workload of rehabilitation physicians. A parallel wrist rehabilitation robot (PWRR) driven by two pneumatic actuators is developed in this paper, consisting of two rotational degrees of freedom for the movements of flexion/extension (F/E) and radial/ulnar deviation (R/U). All components connected to the forearm or the wrist adopt an open structure to improve the wearable convenience, and the PWRR is suitable for most patients, especially those with hypertonia. To determine the PWRR range of motion, the physiological motion space (PMS) of the wrist joint in autonomous and boundary elliptical movements is measured with the help of a VICON motion capture system. The PMS in boundary motions processes an elliptical shape, and the ulnar deviations occupy the most range of motion. The theoretical workspace (TWS) of PWRR is then calculated and designed based on the kinematic model and the distribution characteristics of PMS. In addition, two indices are introduced to evaluate the kinematic performance of PWRR. A PWRR prototype is developed based on the optimal geometrical parameters and detailed structures. Its effective workspace (EWS), which has more clinical significance, is acquired by measuring the F/E and R/U movements during autonomic movements. The EWS, is smaller than TWS due to the physical structure, volume, and interference of mechanical elements. Besides, EWS can nearly encircle PMS, and satisfies all single-axis rehabilitations and compound motions of the wrist complex. The two indices, motion isotropy da and condition number κ, within TWS change smoothly with no mutation, suggesting that PWRR is sufficiently kinematically isotropic, and has no singularity configuration. The analysis shows that the developed PWRR can be applied widely in the wrist rehabilitation.

A four-limb parallel Schönflies motion generator with full-circle end-effector rotation

This paper presents a four-limb parallel Schönflies motion generator for the pick-and-place application, whose end-effector is composed of a planetary gear train as the amplification mechanism to realize the full-circle rotation. The kinematic aspects, including the workspace, dexterity and singularity, are analyzed and evaluated. The singular configurations and the singularity loci are identified both graphically and numerically, which shows that the singular configurations of the manipulator can be avoided by keeping all the limbs working in a prescribed working mode together with the end-effector rotation in a clockwise direction from the neutral orientation. Moreover, the dexterity evaluation is carried out to depict the workspace quality and dexterous working envelope. It turns out that the proposed robot admits a super-ellipsoidal workspace with the full-circle rotation of the end-effector, suitable for pick-and-place operations. Finally, robot dynamics is considered to select the actuators.

Lie Group Based Type Synthesis Using Transformation Configuration Space for Reconfigurable Parallel Mechanisms With Bifurcation Between Spherical Motion and Planar Motion

Abstract This paper investigates novel reconfigurable parallel mechanisms with bifurcation between planar subgroup SE(2) and rotation subgroup SO(3) based on a transformation configuration space. Having recollected necessary theoretical fundamentals with regard to compositional submanifolds and kinematic bonds, the motion representation of the platform of reconfigurable parallel mechanisms are investigated. The transformation configuration space of a reconfigurable parallel mechanism with motion branches is proposed with respect to the fact that the intersection of Lie subgroups or submanifolds is the identity element or a non-identity element. The switch conditions of the transformation configuration space are discussed, leading to establishment of a theoretical foundation for realizing a switch of motion branches. The switch principle of reconfigurable parallel mechanisms is further investigated with respect to the common motion between SE(2) parallel-mechanism motion generators and SO(3) parallel-mechanism motion generators. Under this principle, the subchains with common motion generators are synthesized and divided into two types of generators. The first type of generators generates kinematic chains with a common intersection of three joint axes, and the second type of generators generates a common intersection of two joint axes. Following this, two types of reconfigurable parallel mechanisms with three identical subchains are synthesized, resulting in 11 varieties in which platforms can be switched between SE(2) and SO(3) after passing through the singularity configuration space.

Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background

We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a monopole-anti-monopole pair of magnetic charge $\pm Q$ separated by a distance $s$ in a periodic $L^3$ lattice, and study the low-lying eigenvalues of different lattice Dirac operators under a continuum limit defined by taking $L\to\infty$ at fixed $s/L$. As the background gauge field is parity even, we look for a two-fold degeneracy of the Dirac spectrum that is expected of a continuum-like Dirac operator. The naive-Dirac operator exhibits such a parity-doubling, but breaks the degeneracy of the fermion-doubler modes for the $Q$ lowest eigenvalues in the continuum limit. The Wilson-Dirac operator lifts the fermion-doublers but breaks the parity-doubling in the $Q$ lowest modes even in the continuum limit. The overlap-Dirac operator shows parity-doubling of all the modes even at finite $L$ that is devoid of fermion-doubling, and singles out as a properly regulated continuum Dirac operator in the presence of singular gauge field configurations albeit with a peculiar algorithmic issue.

Premature failures in standard test specimens with composite materials induced by stress singularities in adhesive joints

This work presents three examples of standard test configurations, involving composite materials, where the presence of stress singularities induced by adhesive joints causes premature failures leading to underestimated strength values. Slight modifications of the local geometry, removing or reducing, in these critical points, the order of the stress singularities, have shown to give higher experimental failure loads, with almost double failure loads in the most striking cases.The three examples analyzed in the present work are: a) the tensile and shear strength determination of a bimaterial interface, b) the off-axis tension test, for the intralaminar shear strength of unidirectional long fibre composite materials and c) the compression test of thick composite laminates. In two of the three cases, the premature failure occurs at the corner where the tab (which is necessary for the grip jaw faces of the testing machine) is bonded to the composite laminate, while in the third one the failure occurs at the bimaterial interface of the two materials, all of them involving an adhesively bonded joint and corner configurations with stress singularities.With the use of a semi-analytical tool, developed by the authors, to calculate the order of stress singularities, slight and very local geometrical modifications have been successfully carried out to eliminate the stress singularity configuration. After the modifications, higher failure loads have been obtained in the tests carried out.The major outcome of the present work is the role that the singular stresses play in the premature failure of standard tests involving adhesive bonding. A correlation between the removal of the singularity stress configuration in critical parts of the samples and a higher experimental failure load, in all studied cases, has been clearly shown.

Universality of annihilation barriers of large magnetic skyrmions in chiral and frustrated magnets

Magnetic skyrmions are whirls in the magnetization whose topological winding number promises stability against thermal fluctuations and defects. They can only decay via singular spin configurations. We analyze the corresponding energy barriers of skyrmions in a magnetic monolayer for two distinct stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and competing interactions. Based on our numerically calculated collapse paths on an atomic lattice, we derive analytic expressions for the saddle point textures and energy barriers of large skyrmions. The sign of the spin stiffness and the sign of 4th-order derivative terms in the classical field theory determines the nature of the saddle point and thus the height of the energy barrier. In the most common case for DMI-stabilized skyrmions, positive stiffness and negative 4th-order term, the saddle point energy approaches a universal upper limit described by an effective continuum theory. For skyrmions stabilized by frustrating interactions, the stiffness is negative and the energy barrier arises mainly from the core of a singular vortex configuration.

Simultaneous Control of Two Points for Snake Robot and Its Application to Transportation

This letter presents a simultaneous trajectory tracking control method for two points of a snake robot. The kinematic model considering two regulated points is determined as a switched system that is switched by lifting a few wheels. The system becomes a kinematically redundant system by the lifting of the wheels; however, it has to prevent two types of singular configurations; one is the traditional one, and the other is caused by regulating two points simultaneously. Using this redundancy and selecting the lifted wheels, we design a trajectory tracking controller for two points by preventing the two types of singular configurations. The effectiveness of the proposed control method was demonstrated by tracking experiments as well as applications, namely, the transportation of an object by caging manipulation and the steering of a handcart.

A 3-R(SRS)RP Multi-Loop Mechanism for Space Manipulation: Design, Kinematics, Singularity, and Workspace

Abstract Space manipulation has great prospects in aerospace applications. In this work, a multiloop robot, namely 3-R(SRS)RP multiloop mechanism, is presented. Its design, kinematics, singularity, and workspace are studied. The novel design is mainly reflected in the robot’s structure, variable section, and novel compound hinge. Given these features, the forward-displacement undertaken with a closed-loop method leads to a complex mapping diagram. Only numerical solutions are obtained in this model due to the variable section parameter λ. This variable affects kinematic performances such as bending and folding properties. Moreover, the node differential kinematics and the Jacobian matrix are solved to analyze singular configurations of the mechanism. The workspace is then evaluated via a numerical method with varying λ. The bending and folding properties and the continuous workspace of the given robot vary while changing λ. Hence, the robot has great potentials of good performances in various applications. With this robot, a multimodule manipulator with a wide range of operations, increased mobility and rigidity, variable geometry, and adaptable shape based on mission requirements can be constructed.

Design and Analysis of a Novel Planar Translational Parallel Robotic Mechanism with Three Limbs

A novel planar translational parallel robotic mechanism with three limbs is designed. The degree of freedom (DOF) and output characteristics of mechanism are studied based on the screw theory. The mathematic models including position, velocity and acceleration are derived according to different forms of the actuated inputs. When the linear displacements of two cylindrical joints are selected as the actuated inputs, the velocity Jacobian is an identity matrix and the mechanism has fully isotropic kinematics characteristics. Singularity of the mechanism is discussed and all singular configurations are explored. Finally, kinematics simulation of the mechanism is carried out by ADMAS and MATLAB software, and the kinematic curves are drawn.

Kinematic analysis and dimensional optimization of a 2R2T parallel manipulator

The need of a device providing two-translational and two-rotational movements led us to design a 3UPS–1RPU parallel manipulator. The manipulator consisted of a mobile platform connected to a base through one central leg and three external legs located at the same radial distance. By studying different locations of the legs anchoring point, we improved the first layout design, yet not the optimal one. On this basis, this paper focuses on the optimal dimensional design of the manipulator. To this end, we put forward the kinematics equations of the manipulator in accordance with the anchoring points coordinates. Through a numerical approach, the equations allowing to find the manipulator workspace are developed. Also, we find a global manipulability index using a local dexterity measure. The latter index serves as an optimal function. The optimization process considers joint constraints. Thus, we built a nonlinear optimization problem solved through sequential quadratic programming algorithms. We start by optimizing only a small set of parameters rather than the entire set, which gives us insights into the initial guess to optimize using the entire set. Findings show that the optimal design approach improves the dexterity of the manipulator and reduces the number of singular configurations while having almost the same workspace as the original layout.

Simplification of Motion Generation in the Singular Configuration of a Wheel-Legged Mobile Robot

Simplification of Motion Generation in the Singular Configuration of a Wheel-Legged Mobile Robot

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.

Dynamic Near-Optimal Control Allocation for Spacecraft Attitude Control Using a Hybrid Configuration of Actuators

This paper proposes a novel dynamic near-optimal control allocation scheme with combination of a saturated baseline controller for spacecraft attitude control using single-gimbal control moment gyros (CMGs) and reaction wheels. First, a saturated controller is proposed to stabilize the nominal system in the presence of actuation mismatch. Aided by a state-dependent variable, a dynamic control allocator is then proposed that allows for smooth switching between two actuation sets. Unlike the previous static constraint optimization formulations, the control allocation augments its performance function with penalty terms in order to enforce individual input constraints and configuration singularity avoidance. Moreover, this dynamic control allocation is implemented with an online update law, which has a modest computational complexity compared to its numerical optimization counterpart. The closed-loop boundedness is guaranteed by a constructive Lyapunov-design method. Simulation results demonstrate that during the attitude maneuvers, the input saturation constraint and the active avoidance of CMG singularities are enforced with a relatively small computational cost.

Adaptive Spacecraft Attitude Control Using Single-Gimbal Control Moment Gyroscopes Without Singularity Avoidance

This paper applies retrospective cost adaptive control (RCAC) to spacecraft attitude control with a rotation-matrix attitude parameterization using constant-speed single-gimbal control moment gyroscopes. Unlike control laws that use torque-steering laws to synthesize torque requests while avoiding gimbal singularities, the adaptive control law requests the rate of each gimbal. Because no torque request is provided, there is no need to invert the mapping from the gimbal rates to the control torque, and thus no attempt is made to avoid gimbal singularities. The RCAC implementation is based on a target model involving a single Markov parameter corresponding to the initial gimbal configuration. The parameters and weights for RCAC are based on nominal-model tuning, which uses no explicit knowledge of the nonlinear equations of motion. This paper investigates the robustness of RCAC to off-nominal conditions of commands, noise, and unknown bus inertia; and it examines the performance of RCAC in the case where an approximately singular gimbal configuration occurs during attitude command, following as well as the case of an initial gimbal-lock singularity. The performance of the adaptive controller in the presence of sensor/actuator misalignment is also investigated.

Application of an augmented Lagrangian approach to multibody systems with equality motion constraints

The focus of this work is on dynamics of multibody systems subject to bilateral motion constraints. First, a new set of equations of motion is employed, expressed as a coupled system of strongly nonlinear second-order ordinary differential equations. After putting these equations in a weak form, the position, velocity and momentum type quantities are assumed to be independent. This leads to a three-field set of equations of motion. Next, an alternative formulation is developed, based on optimization principles. It is shown that the equations of motion can eventually be cast in a form obtained by application of an augmented Lagrangian formulation, after introducing an appropriate set of penalty terms. This final set of equations is then used as a basis for developing a new time integration scheme. The validity and numerical efficiency of this scheme is verified by applying it to several example systems. In those examples, special emphasis is put on illustrating the advantages of the new method when applied to selected mechanical systems, involving redundant constraints or singular configurations.

Attitude Control of Momentum-Biased Satellites Equipped with Control Moment Gyroscopes

This paper deals with the attitude control problem of a satellite using control moment gyroscopes (CMGs). CMGs usually suffer from singularity problems. A method is proposed using non-zero or biased angular momentum of a satellite to avoid the singularity issue. The key concept of the method is using gyroscopic torque due to the angular momentum as the auxiliary torque. For this purpose, a nonlinear controller is designed using the state-dependent Riccati equation method and it is proven that such a nonlinear controller is possible for certain conditions. Furthermore, the proposed method greatly reduces the number of singularity configurations that are not manageable. Simulation examples show that the proposed method works satisfactorily.

Maximizing the Size of Self-Motion Manifolds to Improve Robot Fault Tolerance

One measure of a robot's fault tolerance is the size of its self-motion manifold. This letter presents a new methodology for finding the largest self-motion manifold(s) of kinematically redundant robots, that consists of two algorithms. Because large self-motion manifolds occur near singular configurations, the first algorithm is designed to identify singularities of all ranks, including high-rank singularities. One unique feature of this algorithm is its ability to deal with the ill conditioned nature of singular vectors when there are multiple nearly equal singular values. The second algorithm is constructed to compute the self-motion manifolds that contain these singular configurations by iteratively moving along the null space of the robot's Jacobian. An important aspect of this computation is to deal with singularities along the manifold, where the null space is high dimensional. These two algorithms are applied to the well-known Mitsubishi PA-10 to illustrate their effectiveness at identifying singularities and computing the largest self-motion manifold(s).

Reliable motion planning for parallel manipulators

Geometric uncertainties may jeopardize the performance of parallel manipulators, especially during motion planning. Recent research demonstrated that, during motion planning and due to uncertainties, manipulators may accidentally assume low performance or singular configurations. Thus, reliable motion planning algorithms are required. Very few algorithms were proposed to avoid such problem in parallel manipulators. This paper presents a reliable motion planning technique. First, failure modes are defined. Then, a Monte Carlo simulation is used to provide information on how the manipulator’s uncertainties affect its conditioning. Based on this simulation, probabilities of failure are computed for several manipulator workspace configurations. After that, an artificial neural network metamodel is trained to overcome Monte Carlo’s computational inefficiency on the failure probability estimation. This metamodel is assessed by an iterative strategy that exploits genetic operators to compute optimal trajectories avoiding regions that are considerably affected by uncertainties. Due to its modular methodology, the technique can be easily adapted for different applications. A 3RRR manipulator is used as a case study.

Kinematic Design Optimization of an Eight Degree-of-Freedom Upper-Limb Exoskeleton

SummaryThis paper studies the problem of optimizing the kinematic structure of an eight degree-of-freedom upper-limb rehabilitation exoskeleton. The objective of optimization is achieving minimum volume and maximum dexterity in the workspace of daily activities specified by a set of upper-arm configurations. To formulate the problem, a new index is proposed for effective characterization of kinematic dexterity for wearable robots. Additionally, a set of constraints are defined to ensure that the optimal design can cover the desired workspace of the exoskeleton, while singular configurations and physical interferences are avoided. The formulated multi-objective optimization problem is solved using an evolutionary algorithm (Non-dominated Sorting Genetic Algorithm II) and the weighted sum approach. Among the resulted optimal points, the point with least sensitivity with respect to the variations of design variables is chosen as the final design.

Kinematics and reliable analysis of decoupled parallel mechanism for ankle rehabilitation

The rehabilitation training is the key process for restoring the normal physiological functions for patients. The rehabilitation robot has been developed for the reason that it can help patient complete the repeated training process. However, most of rehabilitation robots are based on parallel mechanism with coupled motion, which leads to the kinematic complication and unreliability. In order to overcome the weakness resulted from coupled motion, this paper presents a RRR-PaRPS-RHJ type ankle rehabilitation parallel mechanism with three rotation degrees of freedom and motion decoupling function. Firstly, the inverse kinematics results are obtained by using the transformation of coordinates, and the motion decoupling characteristics is analyzed. Then according to the Euler kinematic equations, the Jacobian matrix is computed. On this basis, the singular configuration is analyzed. Finally, the comparative analysis between 3-SPS/S and RRR-PaRPS-RHJ ankle rehabilitation mechanism is performed by ADAMS. The results show that the present mechanism has good kinematic character. It can avoid the driving interference caused by the motion coupling, which improves the comfort and reliability of the training process.