Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai ◽  
Darwin G. Caldwell
Keyword(s):  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Rank Deficiency ◽  
Actuation Redundancy ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Lower Mobility

This paper investigates the behavior of a type of parallel mechanisms with a central strut. The mechanism is of lower mobility, redundantly actuated, and used for sprained ankle rehabilitation. Singularity and dexterity are investigated for this type of parallel mechanisms based on the Jacobian matrix in terms of rank deficiency and condition number, throughout the workspace. The nonredundant cases with three and two limbs are compared with the redundantly actuated case with three limbs. The analysis demonstrates the advantage of introducing the actuation redundancy to eliminate singularities and to improve dexterity and justifies the choice of the presented mechanism for ankle rehabilitation.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism for Rehabilitation

2007 ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai
Keyword(s):  
Control System ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Control System Design ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Moving Platform

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

2006 ◽  
Vol 129 (4) ◽  
pp. 390-396 ◽  
Author(s):  
Si J. Zhu ◽  
Zhen Huang ◽  
Hua F. Ding
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Rear Part ◽  
Lower Mobility ◽  
Acceleration Analysis

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N<6) mechanism, this method can build a square (N×N) Jacobian matrix and cubic (N×N×N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

On the kinematics of a new parallel mechanism with Schoenflies motion

Robotica ◽  
2015 ◽  
Vol 34 (9) ◽  
pp. 2056-2070 ◽  
Author(s):  
Po-Chih Lee ◽  
Jyh-Jone Lee
Keyword(s):  
Closed Form ◽  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Matrix Algebra ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Pick And Place

SUMMARYThis paper investigates the kinematics of one new isoconstrained parallel manipulator with Schoenflies motion. This new manipulator has four degrees of freedom and two identical limbs, each having the topology of Cylindrical–Revolute–Prismatic–Helical (C–R–P–H). The kinematic equations are derived in closed-form using matrix algebra. The Jacobian matrix is then established and the singularities of the robot are investigated. The reachable workspaces and condition number of the manipulator are further studied. From the kinematic analysis, it can be shown that the manipulator is simple not only for its construction but also for its control. It is hoped that the results of the evaluation of the two-limb parallel mechanism can be useful for possible applications in industry where a pick-and-place motion is required.

Kinematic Analysis of a Novel 3-DOF Parallel Mechanism with Actuation Redundancy

2013 ◽  
Vol 816-817 ◽  
pp. 821-824
Author(s):  
Xue Mei Niu ◽  
Guo Qin Gao ◽  
Zhi Da Bao
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Rbf Neural Network ◽  
Analysis Method ◽  
Parallel Kinematic Mechanism ◽  
Redundantly Actuated ◽  
Parallel Kinematic ◽  
Forward Kinematic ◽  
Kinematic Mechanism ◽  
Kinematic Solution

Kinematic analysis plays an important role in the research of parallel kinematic mechanism. This paper addresses a novel forward kinematic solution based on RBF neural network for a novel 2PRRR-PPRR redundantly actuated parallel mechanism. Simulation results illustrate the validity and feasibility of the kinematic analysis method.

Design of a Four Legged Parallel Mechanism to Improve the Dexterity of Walking Robot

2009 ◽  
Author(s):  
ChiHyo Kim ◽  
KunWoo Park ◽  
TaeSung Kim ◽  
MinKi Lee
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Topology Design ◽  
Condition Numbers ◽  
Walking Robots ◽  
Rough Terrain ◽  
Parallel Mechanisms ◽  
Walking Robot ◽  
Intermediate Mechanism

This paper designs a four legged parallel mechanism to improve the dexterity of three layered parallel walking robot. Topology design is conducted for a leg mechanism composed of four legs, base and ground, which constitute a redundant parallel mechanism. This mechanism is subdivided into four sub-mechanism composed of three legs. A motor vector is adopted to determine the 6×8 Jacobian of the redundant parallel mechanism and the 6×6 Jacobian of the sub-mechanisms, respectively. The condition number of the Jacobian matrix is used as an index to measure a dexterity. We analyze the condition numbers of the Jacobian over the positional and orientational walking space. The analytical results show that a sub-mechanism has lots of singularities within workspace but they are removed by a redundant parallel mechanism improving the dexterity. This paper presents a parallel typed walking robot to enlarge walking space and stability region. Seven types of three layered walking robots are designed by inserting an intermediate mechanism between the upper and the lower legged parallel mechanisms. They provide various types of gaits to walk rough terrain and climb over a wall with small degrees of freedom.

CONCEPTUAL DESIGN FOR ROBOT-AIDED ANKLE REHABILITATION DEVICE

2015 ◽  
Vol 76 (12) ◽  
Author(s):  
Muhammad Nazrin Shah Shahrol Aman ◽  
Shafriza Nisha Basah ◽  
Wan Khairunzam Wan Ahmad ◽  
Shahriman Abu Bakar
Keyword(s):  
Parallel Mechanism ◽  
Ankle Injury ◽  
Physical Injury ◽  
Concept Design ◽  
Parallel Mechanisms ◽  
Concept Generation ◽  
Physiotherapy Treatment ◽  
Standard Design ◽  
Ankle Rehabilitation ◽  
Therapy Treatment

Ankle injury is one of physical injury that can happen whether in sports or in domestic accidents. The injury can take from weeks to months to recover and requires physiotherapy treatment for effective recovery. Currently, there are established treatments for ankle rehabilitation in hospital such as endurance training and range-of-motion training. However, the success of rehabilitation for ankle injury directly depends on physiotherapy administered by experts. This conventional therapy treatment requires patients to frequently visit to hospital which is tedious and costly. To solve this, researchers have introduced a number of robot-aided ankle rehabilitation devices which has been developed in the last decade. However, those devices are bulky and do not designed for portability and configurability – which is an important feature for patients undergoing rehabilitation at home. In this paper, we proposed a concept based on robot-aided ankle rehabilitation device to assist patients undergo rehabilitation procedures. We focused on all patients’ need especially based on important features such as portability and configurability of the device. Standard design process were followed including concept generation and concept selection according to all relevant criteria using Morphological Charts and Pugh Method.  A Pulley Driven Cable Based Parallel Mechanism robot-aided ankle rehabilitation device has been selected based on selections from 5 different concept design generated. We show that a design based on parallel mechanisms should provide the needed portability and configurability. This result provides an insight for a portable and configurable robot-aided ankle rehabilitation device.

A Quasi-Static Model for Planar Compliant Parallel Mechanisms

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Cyril Quennouelle ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanism ◽  
Applied Load ◽  
Jacobian Matrix ◽  
Static Model ◽  
Parallel Mechanisms ◽  
Compliance Matrix ◽  
End Effector ◽  
Kinematic Constraints ◽  
Compliant Parallel Mechanism ◽  
External Loads

In this paper, the mobility, the kinematic constraints, the pose of the end-effector, and the static constraints that lead to the kinematostatic model of a compliant parallel mechanism are introduced. A formulation is then provided for its instantaneous variation—the quasi-static model. This new model allows the calculation of the variation in the pose as a linear function of the motion of the actuators and the variation in the external loads through two new matrices: the compliant Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism. Finally, a simple application to a planar four-bar mechanism is presented to illustrate the use of this model and the new possibilities that it opens, notably the study of the kinematics for any range of applied load.

Kinematic Calibration for Redundantly Actuated Parallel Mechanisms

2004 ◽  
Vol 126 (2) ◽  
pp. 307-318 ◽  
Author(s):  
Jay il Jeong ◽  
Dongsoo Kang ◽  
Young Man Cho ◽  
Jongwon Kim
Keyword(s):  
Optimization Algorithm ◽  
Parallel Mechanism ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Geometrical Constraint ◽  
Kinematic Parameters ◽  
Angle Error ◽  
Calibration Algorithm ◽  
Redundantly Actuated

We present a new kinematic calibration algorithm for redundantly actuated parallel mechanisms, and illustrate the algorithm with a case study of a planar seven-element 2-degree-of-freedom (DOF) mechanism with three actuators. To calibrate a nonredundantly actuated parallel mechanism, one can find actual kinematic parameters by means of geometrical constraint of the mechanism’s kinematic structure and measurement values. However, the calibration algorithm for a nonredundant case does not apply for a redundantly actuated parallel mechanism, because the angle error of the actuating joint varies with position and the geometrical constraint fails to be consistent. Such change of joint angle error comes from constraint torque variation with each kinematic pose (meaning position and orientation). To calibrate a redundant parallel mechanism, one therefore has to consider constraint torque equilibrium and the relationship of constraint torque to torsional deflection, in addition to geometric constraint. In this paper, we develop the calibration algorithm for a redundantly actuated parallel mechanism using these three relationships, and formulate cost functions for an optimization algorithm. As a case study, we executed the calibration of a 2-DOF parallel mechanism using the developed algorithm. Coordinate values of tool plate were measured using a laser ball bar and the actual kinematic parameters were identified with a new cost function of the optimization algorithm. Experimental results showed that the accuracy of the tool plate improved by 82% after kinematic calibration in a redundant actuation case.

Workspace Analysis of Parallel Manipulator for Telemicromanipulation Systems

2001 ◽  
Vol 13 (5) ◽  
pp. 488-496 ◽  
Author(s):  
Noriaki Ando ◽  
◽  
Masahiro Ohta ◽  
Kohei Gonda ◽  
Hideki Hashimoto
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Parallel Mechanisms ◽  
Dual Systems ◽  
Position Accuracy ◽  
Control Scheme ◽  
Workspace Analysis ◽  
Manipulator Control ◽  
Vr Simulator

This paper describes the research results on telemicromanipulation systems for microlevel tasks. Because of its better manipulation precision, stiffness and speed characteristics, the parallel mechanism micromanipulator was chosen to compose our systems. First, the kinematic analysis of our original manipulator mechanism is performed. Then, the structure of our parallel manipulator, control scheme, and experimental results are shown. Position accuracy and device control characteristics are analyzed and the feasibility of the use of parallel mechanisms for micromanipulator is then discussed. A parallel manipulator motion is restricted by 3 factors: mechanical limits of the passive joints, collision between links and actuators limitations. Results of the numerical workspace analysis considering the above factors are shown. We are proposing the use of dual manipulators for implementing improved real manipulation systems. The first kinematics and workspace analysis of dual systems using the VR simulator are also shown.

Analysis and Design of Lower-Mobility Parallel Mechanism of Non-Symmetrical Based on Variable Topology Theory

2011 ◽  
Vol 201-203 ◽  
pp. 1907-1912
Author(s):  
Rong Jiang Cui ◽  
Zong He Guo ◽  
Zi Xun Yin ◽  
Song Song Zhu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Basic Variable ◽  
Analysis And Design ◽  
And Topology ◽  
Variable Topology ◽  
Lower Mobility ◽  
Branched Chain ◽  
Mechanism Theory

First, the branched-chain of parallel mechanism was Classified according to reciprocal screw theory. Then, the introduction of variable topology mechanism theory, with the characteristics of parallel mechanisms themselves, the definition and basic variable topology means of variable topology parallel mechanism were given. With evolutionary theory, the method to design lower-mobility parallel mechanisms of non-asymmetric was proposed based on variable topology mechanism theory .Taking 3-RPS as ideal mechanism and topology synthesis was carried out, besides 2-RPS mechanism were analyzed. The introduction of variable topology mechanism theory provided a theoretical basis and innovative approaches for the synthesis configuration of Lower-mobility parallel mechanisms of non-asymmetric.

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