A Study of the Singular Configurations of Serial Manipulators

1987 ◽  
Vol 109 (1) ◽  
pp. 14-20 ◽  
Author(s):  
Shih-Liang Wang ◽  
Kenneth J. Waldron
Keyword(s):  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Singular Configuration ◽  
Six Degree Of Freedom ◽  
Joint Motions ◽  
Robotic Applications

A manipulator is at a singular configuration when the screws representing the instantaneous joint motions of the manipulator are linearly dependent, and the manipulator cannot be moved along an exact path with specified orientation in world coordinates. There are ∞3 singular configurations for a six-degree-of-freedom manipulator, and all these configurations constitute the singularity field. An algorithm is derived to trace the singularity field. Another algorithm presented in this paper finds all the joint screws reciprocal to a given wrench screw. Some new robotic applications are then possible using the principle of aligning a power tool with the screw of the reciprocal wrench.

Feasible Motion Solutions for Serial Manipulators at Singular Configurations

2003 ◽  
Vol 125 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Yuefa Fang ◽  
Lung-Wen Tsai
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Full Rank ◽  
Joint Space ◽  
Serial Manipulators ◽  
First Order ◽  
Singular Configurations ◽  
Cartesian Space ◽  
Novel Approach ◽  
Singular Configuration

When a serial manipulator is at a singular configuration, the Jacobian matrix will lose its full rank causing the manipulator to lose one or more degrees of freedom. This paper presents a novel approach to model the manipulator kinematics and solve for feasible motions of a manipulator at singular configurations such that the precise path tracking of a manipulator at such configurations is possible. The joint screw linear dependency is determined by using known line varieties so that not only the singular configurations of a manipulator can be identified but also the dependent joint screws can be determined. Feasible motions in Cartesian space are identified by using the theory of reciprocal screws and the resulting equations of constraint. The manipulator first-order kinematics is then modeled by isolating the linearly dependent columns and rows of the Jacobian matrix such that the mapping between the feasible motions in Cartesian space and the joint space motions can be uniquely determined. Finally, a numerical example is used to demonstrate the feasibility of the approach. The simulation results show that a PUMA-type robot can successfully track a path that is singular at all times.

An Approach to Identify Joint Motions for Dynamically Stable Walking

2005 ◽  
Vol 128 (3) ◽  
pp. 649-653 ◽  
Author(s):  
Abhishek Agrawal ◽  
Sunil K. Agrawal
Keyword(s):  
Dynamic Stability ◽  
Biped Robot ◽  
Degree Of Freedom ◽  
Stability Criteria ◽  
Biped Robots ◽  
Wheeled Robots ◽  
Novel Approach ◽  
Six Degree Of Freedom ◽  
Joint Motions

Biped robots are more versatile than conventional wheeled robots, but they tend to tip over easily. The dynamic stability of a biped robot needs to be maintained during walking. In this paper, a novel approach to compute dynamically stable walking motions of a planar six degree-of-freedom biped is presented. This approach is analytical and is based on the need for periodicity of the motion. The resulting gait satisfies the dynamic stability criteria. Sets of joint motions for different step sizes and speed of walking, i.e., quasi-statically and dynamically stable walking patterns, can be obtained.

A Differential-Geometric Analysis of Singularities of Point Trajectories of Serial and Parallel Manipulators

1998 ◽  
Vol 123 (1) ◽  
pp. 80-89 ◽  
Author(s):  
Ashitava Ghosal ◽  
Bahram Ravani
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Rate Of Change ◽  
Degree Of Freedom ◽  
Task Space ◽  
Singular Configurations ◽  
Point Trajectories ◽  
Singular Configuration ◽  
Three Degree Of Freedom ◽  
Derivatives Of

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, the possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

scholarly journals Analysis of Singular Configuration of Robotic Manipulators

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2189
Author(s):  
Xinglei Zhang ◽  
Binghui Fan ◽  
Chuanjiang Wang ◽  
Xiaolin Cheng
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Joint Angle ◽  
Robotic Manipulators ◽  
Jacobian Determinant ◽  
End Effector ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Manipulability Measure ◽  
Singular Configuration

Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

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