scholarly journals A Recursive Method for Finding Revolute-Jointed Manipulator Singularities

1995 ◽  
Vol 117 (1) ◽  
pp. 55-63 ◽  
Author(s):  
J. W. Burdick
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Industrial Robot ◽  
Recursive Algorithm ◽  
Explicit Construction ◽  
Recursive Method ◽  
Matrix Elements ◽  
Screw Axis ◽  
Computational Burden ◽  
Singular Configurations

A geometric application of screw theory is used to develop a recursive algorithm for computing all singular configurations of revolute-jointed manipulators with arbitrary link geometries and an arbitrary number of joints. The depth of the recursion is linear in the number of joints, n, while the computational burden is proportional to 2n−2. This method does not require explicit construction of the Jacobian matrix elements or a determinant operation. The method is also robust with respect to the bifurcations that occur for industrial robot geometries. Further, the screw axis of the singular motion is determined at no additional cost.

A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Kefei Wen ◽  
TaeWon Seo ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Singular Configurations ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

2003 ◽  
Author(s):  
Hee-Byoung Choi ◽  
Atsushi Konno ◽  
Masaru Uchiyama
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Loop Structure ◽  
Singular Configurations ◽  
Planning And Control ◽  
Kinematic Singularities ◽  
And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

SCREW-THEORY BASED METHODS FOR SOLVING THE INVERSE INSTANTANEOUS KINEMATICS OF 6 DOF MANIPULATORS

1992 ◽  
Vol 16 (1) ◽  
pp. 1-15
Author(s):  
R.G. Fenton ◽  
Xiaolun Shi
Keyword(s):  
Computational Efficiency ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Decomposition Methods ◽  
Joint Position ◽  
End Effector ◽  
Singular Configurations ◽  
Position Errors

Determination of joint velocities from a given Jacobian matrix and end-effector velocities requires an efficient and accurate algorithm. In this paper, two methods are introduced for this purpose, and compared with three existing methods on the basis of computational efficiency, accuracy, sensitivity to joint position errors and near-degenerate configurations, and capability of dealing with singular configurations. It is found that the two sequential screw-decomposition methods based on Gram-Schmidt Decompositions are the most efficient and computationally accurate methods, and they can also be effectively utilized to cope with singular configurations of the manipulators.

Analysis of Five-Degree-of-Freedom Robot Arms

1983 ◽  
Vol 105 (1) ◽  
pp. 23-27 ◽  
Author(s):  
K. Sugimoto ◽  
J. Duffy
Keyword(s):  
Arc Welding ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Industrial Robot ◽  
Degree Of Freedom ◽  
Numerical Example ◽  
Robot Arms ◽  
Special Cases ◽  
Computer Controlled ◽  
Five Axes

Many kinds of robot arms with five degrees of freedom are widely used in industry for arc welding, spray painting, assembling etc. It is necessary to be able to compute joint displacements when such devices are computer controlled. A solution to this problem is presented and the analysis is illustrated by a numerical example using the most common industrial robot with five axes. Further, special cases are discussed using screw theory.

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.

Generation of Noncircular Bevel Gears With Free-Form Tooth Profile and Curvilinear Tooth Lengthwise

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Fangyan Zheng ◽  
Lin Hua ◽  
Xinghui Han ◽  
Dingfang Chen
Keyword(s):  
Screw Theory ◽  
Mapping Method ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Free Form ◽  
Arc Length ◽  
Screw Axis ◽  
Bevel Gears ◽  
Generating Method ◽  
Instant Screw Axis

Noncircular bevel gear is applied to intersecting axes, realizing given function of transmission ratio. Currently, researches are focused mainly on gear with involute tooth profile and straight tooth lengthwise, while that with free-form tooth profile and curvilinear tooth lengthwise are seldom touched upon. Based on screw theory and equal arc-length mapping method, this paper proposes a generally applicable generating method for noncircular bevel gear with free-form tooth profile and curvilinear tooth lengthwise, covering instant screw axis, conjugate pitch surface, as well as the generator with free-form tooth profile and curvilinear tooth lengthwise. Further, the correctness of the proposed method is verified through illustrations of computerized design.

Concepts of Augmented Image Space and Transformed Feature Space for Efficient Visual Servoing of an “Eye-in-Hand Robot”

Robotica ◽  
1991 ◽  
Vol 9 (2) ◽  
pp. 203-212 ◽  
Author(s):  
Won Jang ◽  
Kyungjin Kim ◽  
Myungjin Chung ◽  
Zeungnam Bien
Keyword(s):  
Visual Feedback ◽  
Visual Servoing ◽  
Industrial Robot ◽  
Robot Vision ◽  
Feature Space ◽  
Image Features ◽  
Image Space ◽  
Formal Definition ◽  
Computational Burden ◽  
Definition Of

SUMMARYFor efficient visual servoing of an “eye-in-hand” robot, the concepts of Augmented Image Space and Transformed Feature Space are presented in the paper. A formal definition of image features as functionals is given along with a technique to use defined image features for visual servoing. Compared with other known methods, the proposed concepts reduce the computational burden for visual feedback, and enhance the flexibility in describing the vision-based task. Simulations and real experiments demonstrate that the proposed concepts are useful and versatile tools for the industrial robot vision tasks, and thus the visual servoing problem can be dealt with more systematically.

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.

A New Index of Static Actuation Force Sensitivity of Mechanisms Based on Unified Forward Jacobian Matrix

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Xu Wang ◽  
Weizhong Guo ◽  
Youcheng Han
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Constraints ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Actuation Force ◽  
Force Sensitivity ◽  
Differential Operation ◽  
Static Equation ◽  
Pose Optimization

Abstract This paper proposes a novel performance index, which is called static actuation force sensitivity (SAFS), to investigate the response of the actuation forces when the amplitude of the suffered load of the end-effector has a change. Smaller SAFS can protect the actuations, and the load is mainly suffered by the structural constraints. This work starts with the construction of the unified forward Jacobian matrix of both serial and parallel mechanisms by screw theory. Then, with the forward Jacobian matrix, the inverse static equation is established. SAFS is thus introduced by the “partial differential” operation on the inverse static equation. SAFS is only related to the position of the whole mechanism and the direction of the suffered load, but not related to the detailed value of the amplitude of the load and the detailed value of the actuation forces; thus, SAFS can reveal the essence of static force capacities of the mechanisms. The example mechanism (namely, the 3revolute-prismatic-spherical (RPS) parallel mechanism) is used to illustrate the distribution of SAFS both over the workspace and at a certain pose. The analysis method of SAFS and the proposed index are expected to be applied to the pose optimization in the motion planning of the mechanisms to protect the actuations.

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