Complete, Minimal and Continuous Kinematic Error Models of Perfect Multi-DOF Joints for Parallel Manipulators

Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. In order to get a better calibration result, the error model should satisfy complete, minimal and continuous criteria. In order to meet the complete requirement, the multi degree-of-freedom (DOF) joints, such as universal or spherical joint in parallel robots, have to be regarded as serial chains formed by multiple independent single DOF joints, such that the manufacturing errors of these joints can be considered. However, several previous work found that these manufacturing errors for some parallel manipulators have little effect on the accuracy improvement. Besides, considering these kind of errors will cause the kinematics to be much more complicated. Therefore, under the assumptions of perfectly manufactured universal, spherical and cylinder joints, a complete, minimal and continuous (CMC) error model is presented in this paper. The identifiability of the kinematic errors of these multi-DOF joints are analytically analyzed. In order to verify the correctness and effectiveness of the proposed method, a numerical simulation of kinematic calibration is conducted on a 6-UPS parallel manipulator. The calibration result is also compared to the one derived from the error model with 138 error parameters. Since the error model and calibration methods are described uniformly, it can be applied to most parallel manipulators.

Task-Based Knee Rehabilitation With Assist-as-Needed Control Strategy and Recovery Tracking System

This research aims to design and implement a novel task-based knee rehabilitation strategy through kinematic synthesis, assist-as-needed control strategy, and recovery tracking system. Experimental kinematic data collected through motion capture system are utilized as an input to the mechanism synthesis procedure. Parallel mechanisms with single degree-of-freedom are considered to generate the complex three-dimensional (3D) motions of the lower leg. An exact workspace synthesis approach is utilized, in which the implicit description of the workspace is made to be a function of the structural parameters of the serial chains of the parallel mechanism, making it easy to relate those parameters to the desired trajectory from the motion capture. The synthesis procedure resulted an exoskeleton which can guide the complex motion of the human knee without the need of mimicking the joint by the exoskeleton counterpart. This can potentially reduce the improper alignment problems arising due to the constantly varying axis of rotation of human joint, which is often very difficult to predict. An assist-as-needed control and recovery tracking strategy is outlined based on an electromyography (EMG) signals and force sensing resistors (FSRs) mounted on the user and exoskeleton, respectively. The EMG signal is captured from the user leg and FSRs are applied at the attachment area of the exoskeleton and the leg, this helps to get the amount of force applied by the exoskeleton to the leg as well as for the recovery tracking. The assist-as-needed controller eliminates the need of constant supervision, and hence saves time and reduces cost of the rehabilitation process. Similarly, the real-time progress tracking system will motivate and actively engage users

Degree of Freedom and Dynamic Analysis of the Multi-Loop Coupled Passive-Input Overconstrained Deployable Tetrahedral Mechanisms for Truss Antennas

Recently, the truss antennas with deployable tetrahedron unit mechanisms have been successfully applied in orbit, owing to the advantages of large calibers, high accuracy, and large folding ratios. As multiloop coupled mechanisms, deployable tetrahedral mechanisms have multiple different output links, whose supporting limbs connecting output links and the base are mutually coupled. These mechanisms are also called the passive-input overconstrained mechanisms because their passive torsion springs are used as drivers and because the number of the drivers contained is more than the degrees of freedom (DOFs). In this work, a method based on the equivalent concept of first link-removing and then restoring is proposed for the DOF analysis of the multiloop coupled deployable tetrahedral mechanisms. With one coupled chain removed, the equivalent serial chains between the coupled components and the base are established in the remainder of the mechanisms. Then, the coupled chain removed is restored and the equivalent of the multiloop coupled mechanisms is obtained. The Lagrange method is used to establish the dynamic equation of the passive-input overconstrained mechanisms; the influence of the stiffness and number of torsion springs on the unfolding motion is examined.

Simulación del Modelo Matemático de la Cinemática Diferencial de Robots Seriales Planos Configuración RRR y RPR

This article presents the model and simulation of the serial robot configurations of the types RRR and RPR, applying the theories of differential kinematics, to obtain the representation of its mathematical model (Jacobian matrix) and its simulation. The differential kinematics in robotics is the relationship between vector spaces, so it is possible to make the velocity map in the joint space in the end effector workspace. We present the differential kinematic model that is obtained from the position kinematics by differentiation techniques and with the help of the asymmetric matrix we obtain the information that is part of the Jacobian matrix, which allows us to know the velocities of the joint variables as a function of linear and angular velocity in the end effector and vice versa. The simulation of the manipulators is carried out validating the mathematical differential model; through the validation of the differential kinematics of serial chains it is possible to apply the procedure to complicated manipulator robots. The method presented here is the basis of a useful tool for solving complex robots, as in the case of redundant, parallel and hybrid serial manipulator robots.

On the Kinematic Performance of a Novel 5-DOF Reconfigurable Hybrid Manipulator With Ultra Large Workspace for Automatic Perfusion of a Large-Scale Spherical Honeycomb Structure

A conventional parallel manipulator consists of a moving platform, a fixed base platform, as well as several serial chains that connect the two platforms. This paper presents a novel five degree-of-freedom (DOF) hybrid manipulator such that its base platform itself is movable and thus reconfigurable. This hybrid structure greatly expands the workspace of the end-effector platform so that it can reach and perform tasks over a large-scale spherical honeycomb structure. First, the inverse kinematics as well as the Jacobian matrix is developed. Then, the workspace and singularity of the hybrid manipulator are studied for four different positions of the reconfigurable base platform to show the enlarged singularity-free workspace. For a large-scale honeycomb structure with prefusion requirements, which is placed within the workspace of the hybrid manipulator, the minimum and maximum limit positions of the reconfigurable base are obtained. Finally, a simulation model for the hybrid manipulator is developed using Mathematica and Adams and numerical simulations are conducted to evaluate the kinematic performance and verify the effectiveness of the hybrid manipulator.

Design of a Novel Task-Based Knee Rehabilitation Exoskeleton Device

This study is aimed at the design of a novel task-based knee rehabilitation device. The desired trajectories of the knee have been obtained through a vision-based motion capture system. The collected experimental kinematic data has been used as an input to a spatial mechanism synthesis procedure. Parallel mechanisms with single degree-of-freedom (DOF) have been considered to generate the complex 3D motions of the lower leg. An exact workspace synthesis approach is utilized, in which the parameterized forward kinematics equations of each serial chains of the parallel mechanisms are to be converted into implicit equations via elimination. The implicit description of the workspace is made to be a function of the structural parameters of the serial chain, making it easy to relate those parameters to the desired trajectory. The selected mechanism has been verified for the accuracy of its trajectory through CAD modeling and simulations. This design approach reduces alignment and fitting challenges in an exoskeleton as the mechanism does not require alignment of each robotic joint axis with its human counterpart.

Kinematic modeling of a 7-degree of freedom spatial hybrid manipulator for medical surgery

The prime objective of this work is to deal with the kinematics of spatial hybrid manipulators. In this direction, in 1955, Denavit and Hartenberg proposed a consistent and concise method, known as D-H parameters method, to deal with kinematics of open serial chains. From literature review, it is found that D-H parameter method is widely used to model manipulators consisting of lower pairs. However, the method leads to ambiguities when applied to closed-loop, tree-like and hybrid manipulators. Furthermore, in the dearth of any direct method to model closed-loop, tree-like and hybrid manipulators, revisions of this method have been proposed from time-to-time by different researchers. One such kind of revision using the concept of dummy frames has successfully been proposed and implemented by the authors on spatial hybrid manipulators. In that work, authors have addressed the orientational inconsistency of the D-H parameter method, restricted to body-attached frames only. In the current work, the condition of body-attached frames is relaxed and spatial frame attachment is considered to derive the kinematic model of a 7-degree of freedom spatial hybrid robotic arm, along with the development of closed-loop constraints. The validation of the new kinematic model has been performed with the help of a prototype of this 7-degree of freedom arm, which is being developed at Council of Scientific & Industrial Research–Central Scientific Instruments Organisation Chandigarh to aid the surgeon during a medical surgical task. Furthermore, the developed kinematic model is used to develop the first column of the Jacobian matrix, which helps in providing the estimate of the tip velocity of the 7-degree of freedom manipulator when the first joint velocity is known.

Biped 4-UPU Parallel Mechanism

A novel biped robot based on a 4-UPU (universal-prismatic-universal) parallel mechanism with actuation redundancy is presented. The biped robot consists of two platforms and four UPU serial chains as limbs. The actuation method of the mechanism is determined based on the mobility and singularity analysis. The singular positions of the mechanism are identified and then eliminated using a redundant actuator. To meet different requirements, the multiple motion modes of the robot are discussed and simulated in the gait analysis. Moreover, the robot has special gaits for reset and self-rescue if overturned. Kinematic analysis of the mechanism and walking stability analysis are carried out in detail. Physical prototype experiments indicate that the proposed biped robot is feasible. Through properly planning the motion modes, the biped robot can quickly pass through rugged terrain containing slopes and obstacles.

Design of a Linkage System to Write in Cursive

This paper presents a design methodology for a system of linkages that can trace planar Bezier curves that represent cursive handwriting of the alphabet and Chinese characters. This paper shows that the standard degree n Bezier curve can be reparameterized so that it takes the form of a trigonometric curve that can be drawn by a one degree-of-freedom coupled serial chain consisting of 2n links. A series of cubic Bezier curves that define a handwritten name yields a series of six-link coupled serial chains that trace these curves. We then show how to simplify this system using cubic trigonometric Bezier curves to obtain a series of four-link serial chains that approximate the system of Bezier curves. The result is a methodology for the design of a mechanical system that draws complex plane curves such as the cursive alphabet and Chinese characters.

Design of Mechanisms to Draw Trigonometric Plane Curves

This paper describes a mechanism design methodology that draws plane curves which have finite Fourier series parameterizations, known as trigonometric curves. We present three ways to use the coefficients of this parameterization to construct a mechanical system that draws the curve. One uses Scotch yoke mechanisms for each of the terms in the coordinate trigonometric functions, which are then added using a belt or cable drive. The second approach uses two-coupled serial chains obtained from the coordinate trigonometric functions. The third approach combines the coordinate trigonometric functions to define a single-coupled serial chain that draws the plane curve. This work is a version of Kempe's universality theorem that demonstrates that every plane trigonometric curve has a linkage which draws the curve. Several examples illustrate the method including the use of boundary points and the discrete Fourier transform to define the trigonometric curve.