Analytic Formulation of Reciprocal Screws and Its Application to Nonredundant Robot Manipulators

2003 ◽  
Vol 125 (1) ◽  
pp. 158-164 ◽  
Author(s):  
Doik Kim ◽  
Wan Kyun Chung
Keyword(s):  
Algebraic Equation ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
The Given ◽  
Pseudo Inverse

One of the most important and widely used concepts in the kinematic analysis of robot manipulators is the reciprocal screw. However, there are no general expressions and easy methods to obtain the reciprocal screw in an analytic manner. This paper suggests an analytic formulation of the reciprocal screws of arbitrarily aligned screw systems. Since the reciprocal screws obtained in this paper are represented by the direction vectors and the position vectors of the given screws, we can analyze the relation between the reciprocal screw system and the given screw system easily. With the results, to find a reciprocal screw is to solve an algebraic equation of the corresponding system of screws. In order to show the usefulness of the result, several examples related to the robot manipulator are provided. For a nonredundant serial manipulator, the pseudo inverse of the Jacobian matrix is shown to be equivalent to the wrench matrix obtained by the reciprocity. For a parallel manipulator, a leg is isolated to obtain an independent part from the manipulator and is analyzed analytically. The proposed method can be applied to any arbitrarily aligned screw system.

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.

scholarly journals A Parallel Manipulator with Planar Configurable Platform and Three End-Effectors

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Jesus H. Tinajero-Campos
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Terminal Link ◽  
Planar Parallel Manipulator ◽  
End Effectors ◽  
Newton Homotopy

This work reports on the kinematic analysis of a planar parallel manipulator endowed with a configurable platform assembled with six terminal links serially connected by means of revolute joints. This topology allows the robot manipulator to dispose of three relative degrees of freedom owing to the mobility of an internal closed-loop chain. Therefore, the proposed robot manipulator can admit three end-effectors. The forward displacement analysis of the configurable planar parallel manipulator is easily achieved based on unknown coordinates denoting the pose of each terminal link. Thereafter, the analysis leads to twelve quadratic equations which are numerically solved by means of the Newton homotopy method. Furthermore, a closed-form solution is available for the inverse position analysis. On the contrary, the instantaneous kinematics of the robot manipulator is investigated by means of the theory of screws. Numerical examples are included with the purpose to illustrate the method of kinematic analysis.

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.

scholarly journals Development of a Robot Manipulator Design for Brain Surgery

2020 ◽  
pp. 48-51
Author(s):  
Didem Guzin ◽  
Erkin Gezgin
Keyword(s):  
System Reliability ◽  
Parallel Manipulator ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Brain Biopsy ◽  
Brain Surgery ◽  
Related Literature ◽  
Manipulator Design ◽  
The Brain ◽  
Spherical Parallel Manipulator

Nowadays, most of the brain surgery operations are carried out by utilizing classical surgery methodologies and equipment. Although related literature includes studies on the robotization of brain surgery systems by the help of technological advancements, these applications mostly focused on the integration of robot manipulators that are designed for industrial automation into the medical area. Thus it can be clearly seen that, there exist lack of robot manipulators that are specifically designed for brain surgery applications, have necessary precision requirements and workspace constraints. In light of this, evaluating its preprototype performance, current study focuses on the improvement of a spherical parallel manipulator structure that was designed for positioning in robotic brain biopsy by taking operation efficiency, system reliability, workspace constraints and ease of manufacturing into consideration.

Dynamical Resolution of Redundancy for Robot Manipulators

1993 ◽  
Vol 115 (3) ◽  
pp. 592-598 ◽  
Author(s):  
A. Ghosal ◽  
S. Desa
Keyword(s):  
Large Class ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Dynamic State ◽  
Redundancy Resolution ◽  
End Effector ◽  
Dynamical Approach ◽  
Pseudo Inverse

A large class of work in the robot manipulator literature deals with the kinematical resolution of redundancy based on the pseudo-inverse of the manipulator Jacobian. In this paper an alternative dynamical approach to redundancy resolution is developed which utilizes the mapping between the actuator torques and the acceleration of the end-effector, at a given dynamic state of the manipulator. The potential advantages of the approach are discussed and an example of a planar 3R manipulator following a circular end-effector trajectory is used to illustrate the proposed approach as well as to compare it with the more well-known approach based on the pseudo-inverse.

scholarly journals Suboptimal approximations in repeatable inverse kinematics for robot manipulators

2017 ◽  
Vol 65 (2) ◽  
pp. 209-217
Author(s):  
I. Duleba ◽  
I. Karcz-Duleba
Keyword(s):  
Configuration Space ◽  
Simulation Study ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Forward Kinematics ◽  
Definition Of ◽  
Pseudo Inverse ◽  
Selection Of

Abstract In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

Kinematic and Singularity Analysis of a Novel 4-DOF Parallel Manipulator

2011 ◽  
Vol 101-102 ◽  
pp. 685-688 ◽  
Author(s):  
Meng Guan ◽  
Yi Min Song ◽  
Tao Sun ◽  
Gang Dong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Velocity Analysis ◽  
Inverse Kinematic Analysis ◽  
In Virtue Of

This paper presents a novel 4-DOF (Degree of Freedom) parallel manipulator called 2-PSS&(2-PRR)R manipulator. Firstly, the architecture of this manipulator is described and the mobility is analyzed via screw theory. Secondly, the inverse kinematic analysis including position analysis and velocity analysis is performed. Finally, the Jacobian matrix is obtained through velocity analysis, and then three kinds of singularity configurations are observed in virtue of the Jacobian matrix. This paper lays the foundation for further research of this manipulator.

Delta robot: Inverse, direct, and intermediate Jacobians

2006 ◽  
Vol 220 (1) ◽  
pp. 103-109 ◽  
Author(s):  
M López ◽  
E Castillo ◽  
G García ◽  
A Bashir
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Kinematic Chain ◽  
End Effector ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Delta Robot ◽  
Intermediate Jacobian

In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, several undesirable postures of the manipulator have been extracted. The analysis of the inverse Jacobian matrix reveals that singularities are encountered when the limbs belonging to the same kinematic chain lie in a plane. Two of the possible configurations which correspond to this condition are when the robot is completely extended or contracted, indicating the boundaries of the workspace. Singularities associated with the direct Jacobian matrix, which correspond to relatively more complicated configurations of the manipulator, have also been derived and commented on. Moreover, the idea of intermediate Jacobian matrices have been introduced that are simpler to evaluate but still contain the information of the singularities mentioned earlier in addition to architectural singularities not contemplated in conventional Jacobians.

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