Kinematics of a 5-axis hybrid robot near singular configurations

2022 ◽  
Vol 75 ◽  
pp. 102294
Author(s):  
Qi Liu ◽  
Wenjie Tian ◽  
Bin Li ◽  
Yue Ma
Keyword(s):  
Singular Configurations

Jacobian Analysis of a Fully Decoupled Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Central Point ◽  
Special Structure ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Reachable Workspace

This paper presents the Jacobian analysis of a parallel manipulator that has a fully decoupled 4-DOF remote center-of-motion for application in minimally invasive surgery. Owing to the special structure of the manipulator, the Jacobian matrix of the manipulator is expressed as a combination of three special Jacobian matrices, namely the Jacobian of motion space, Jacobian of constraints, and Jacobian of actuations. Based on these Jacobian matrices, the singular configurations of the manipulator are then identified. It shows that the configuration singularity only exists at the central point and the boundary of the reachable workspace of the manipulator.

An Analytical Method for Locating Velocity Instantaneous Centers

1992 ◽  
Author(s):  
Hong-Sen Yan ◽  
Meng-Hui Hsu
Keyword(s):  
Analytical Method ◽  
Degrees Of Freedom ◽  
Coefficient Matrix ◽  
Multiple Degrees Of Freedom ◽  
Singular Configurations ◽  
Special Cases

Abstract An analytical method is presented for locating all velocity instantaneous centers of linkage mechanisms with single or multiple degrees of freedom. The method is based on the fact that the coefficient matrix of the derived velocity equations for vector loops, independent inputs, and instantaneous centers is singular. This approach also works for special cases with kinematic indeterminacy or singular configurations.

Singularity-locus expression of a class of parallel mechanisms

Robotica ◽  
2002 ◽  
Vol 20 (3) ◽  
pp. 323-328 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Polynomial Equation ◽  
Geometric Parameters ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Degree Polynomial ◽  
Singular Configurations ◽  
Singularity Locus ◽  
Orientation Parameters

In parallel mechanisms, singular configurations (singularities) have to be avoided during motion. All the singularities should be located in order to avoid them. Hence, relationships involving all the singular platform poses (singularity locus) and the mechanism geometric parameters are useful in the design of parallel mechanisms. This paper presents a new expression of the singularity condition of the most general mechanism (6-6 FPM) of a class of parallel mechanisms usually named fully-parallel mechanisms (FPM). The presented expression uses the mixed products of vectors that are easy to be identified on the mechanism. This approach will permit some singularities to be geometrically found. A procedure, based on this new expression, is provided to transform the singularity condition into a ninth-degree polynomial equation whose unknowns are the platform pose parameters. This singularity polynomial equation is cubic in the platform position parameters and a sixth-degree one in the platform orientation parameters. Finally, how to derive the expression of the singularity condition of a specific FPM from the presented 6-6 FPM singularity condition will be shown along with an example.

A Method of Inverse Kinematics Solution for a Class of Robotic Manipulators

1997 ◽  
Author(s):  
Tuna Balkan ◽  
M. Kemal Özgören ◽  
M. A. Sahir Arikan ◽  
H. Murat Baykurt
Keyword(s):  
Nonlinear Equation ◽  
Analytical Method ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Industrial Robot ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Singular Configurations ◽  
Inverse Kinematics Problem ◽  
Joint Variable

Abstract A semi-analytical method and a computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in wrist point equations. For this case, it becomes possible to express all the joint variables in terms of a joint variable, and this reduces the inverse kinematics problem to solving a nonlinear equation in terms of that joint variable. The solution can be obtained by iterative methods and the remaining joint variables can easily be computed by using the solved joint variable. Since the method is manipulator dependent, the equations will be different for kinematically different classes of manipulators, and should be derived analytically. A significant benefit of the method is that, the singular configurations and the multiple solutions indicated by sign ambiguities can be determined while deriving the inverse kinematic expressions. The developed method is applied to a six-revolute-joint industrial robot, FANUC Arc Mate Sr.

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