Singularity Analysis of Closed Kinematic Chains

1999 ◽  
Vol 121 (1) ◽  
pp. 32-38 ◽  
Author(s):  
F. C. Park ◽  
J. W. Kim
Keyword(s):  
Configuration Space ◽  
Degrees Of Freedom ◽  
Geometric Analysis ◽  
Singularity Analysis ◽  
Geometric Framework ◽  
End Effector ◽  
Kinematic Chains ◽  
Closed Chain ◽  
High Level ◽  
Kinematic Singularities

This paper presents a coordinate-invariant differential geometric analysis of kinematic singularities for closed kinematic chains containing both active and passive joints. Using the geometric framework developed in Park and Kim (1996) for closed chain manipulability analysis, we classify closed chain singularities into three basic types: (i) those corresponding to singular points of the joint configuration space (configuration space singularities), (ii) those induced by the choice of actuated joints (actuator singularities), and (iii) those configurations in which the end-effector loses one or more degrees of freedom of available motion (end-effector singularities). The proposed geometric classification provides a high-level taxonomy for mechanism singularities that is independent of the choice of local coordinates used to describe the kinematics, and includes mechanisms that have more actuators than kinematic degrees of freedom.

Singularity analysis of a 7-DOF spatial hybrid manipulator for medical surgery

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sameer Gupta ◽  
Ekta Singla ◽  
Sanjeev Soni ◽  
Ashish Singla
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Medical Surgery ◽  
Natural Motion ◽  
Hybrid Manipulator ◽  
Contour Plots ◽  
Kinematic Singularities ◽  
And Control ◽  
Optimal Configurations

Abstract This paper presents the singularity analysis of a 7-degrees of freedom (DOF) hybrid manipulator consisting of a closed-loop within it. From the past studies, it is well-known that the kinematic singularities play a significant role in the design and control of robotic manipulators. Kinematic singularities pose two-fold effects – first, they can induce the loss of one or more DOF of the manipulator and cause infinite joint rates at that particular joint, and second, they help to determine the trajectory or zone with high mechanical advantage. In current work, a 7-DOF hybrid manipulator is considered which is being developed at Council Of Scientific And Industrial Research–Central Scientific Instruments Organisation (CSIR–CSIO) Chandigarh to assist a surgeon during a medical-surgical task. To emulate the natural motion of a surgeon, the challenging configuration with redundant DOF is utilized. Jacobian has been computed analytically and analyzed at each instantaneous configuration with the evaluation of manipulability. Effect of a closed loop in the hybrid configurations is focused at, and utilizing the contour plots, good and worst working zones are identified in the workspace of the manipulator. The verification and validation of best and worst manipulability points (singularities) are done with the help of genetic algorithms, to determine locally and globally optimal configurations. Finally, on the basis of the singularity analysis, the present work concludes with few guidelines to the surgeon about the best and worst working zones for surgical tasks.

scholarly journals Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

Robotica ◽  
2014 ◽  
Vol 33 (4) ◽  
pp. 747-767 ◽  
Author(s):  
Masayuki Shimizu
Keyword(s):  
Analytical Method ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Target Orientation ◽  
End Effector ◽  
Position And Orientation

SUMMARYThis paper proposes an analytical method of solving the inverse kinematic problem for a humanoid manipulator with five degrees-of-freedom (DOF) under the condition that the target orientation of the manipulator's end-effector is not constrained around an axis fixed with respect to the environment. Since the number of the joints is less than six, the inverse kinematic problem cannot be solved for arbitrarily specified position and orientation of the end-effector. To cope with the problem, a generalized unconstrained orientation is introduced in this paper. In addition, this paper conducts the singularity analysis to identify all singular conditions.

Manipulability of Closed Kinematic Chains

1998 ◽  
Vol 120 (4) ◽  
pp. 542-548 ◽  
Author(s):  
F. C. Park ◽  
J. W. Kim
Keyword(s):  
Dynamic Characteristics ◽  
Geometric Analysis ◽  
Riemannian Metric ◽  
Kinematic Chains ◽  
Closed Chain ◽  
Invariant Differential ◽  
Practical Algorithm ◽  
Uniform Manner

This paper presents a coordinate-invariant differential geometric analysis of manipulability for closed kinematic chains containing active and passive joints. The formulation treats both redundant and nonredundant mechanisms, as well as over-actuated and exactly actuated ones, in a uniform manner. Dynamic characteristics of the mechanism and manipulated object can also be naturally included by an appropriate choice of Riemannian metric. We illustrate the methodology with several closed chain examples, and provide a practical algorithm for manipulability analysis of general chains.

A Parallelogram-Based Parallel Manipulator for Schönflies Motion

2006 ◽  
Vol 129 (12) ◽  
pp. 1243-1250 ◽  
Author(s):  
Oscar Salgado ◽  
Oscar Altuzarra ◽  
Enrique Amezua ◽  
Alfonso Hernández
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
End Effector ◽  
Fixed Direction ◽  
Axis Parallel ◽  
Schönflies Motion ◽  
4 Degrees Of Freedom

A parallelogram-based 4 degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Schönflies motion that allows the end effector to translate in all directions and rotate around an axis parallel to a fixed direction. The theory of group of displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and an improved stiffness to the manipulator. This paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity, and the singularity analysis. Finally, a prototype of the manipulator, adding some considerations about its singularity-free design, and some technical applications in which the manipulator can be used are presented.

Real-Time Direct Position Analysis of Parallel Spherical Wrists by Using Extra Sensor Data

2004 ◽  
Author(s):  
R. Vertechy ◽  
V. Parenti-Castelli
Keyword(s):  
Real Time ◽  
Measurement Errors ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
The Body ◽  
Least Square ◽  
Sensor Data ◽  
End Effector ◽  
Kinematic Chains ◽  
Position Analysis

The paper presents an algorithm for the real-time evaluation of the actual end-effector orientation (pose) of general parallel spherical wrists. Conceptually, the method relies on the evidence that the pose of a rigid body is defined once the location of at least two linearly independent vectors attached to the body is known. The location of these vectors of the wrist end-effector is determined by the solution of the direct position analysis of some properly chosen kinematic chains (legs) of the manipulator. In order to accomplish this analysis, extra-sensors, which measure suitable non-actuated variables of the chosen legs, need to be placed in addition to the ones normally embedded in the servo motors, i.e. the sensors which measure the actuated variables. From a mathematical point of view, the algorithm is built on the Polar Decomposition of a matrix and has inherent least square features. Thus, together with measurement redundancy, i.e. more sensors (extra-sensors) than the mechanism degrees of freedom, the method also allows minimizing the influence of both round-off and measurement errors on the estimation of the location of the wrist end-effector. The method is general but, in order to prove its effectiveness, without loss of generality it has been customized to the solution of the (3-UPS)S fully parallel wrist architecture. Comparison of the proposed method, in both its general and specialized form, with others from the literature is provided.

Decoupled and Homokinetic Transmission of Rotational Motion via Constant-Velocity Joints in Closed-Chain Orientational Manipulators

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Marco Carricato
Keyword(s):  
Constant Velocity ◽  
Design Parameters ◽  
Motor Drive ◽  
Input Output ◽  
End Effector ◽  
Closed Chain ◽  
Constant Velocity Joints ◽  
Kinematic Singularities ◽  
Analytical Expressions ◽  
Derivatives Of

This paper presents novel 2DOF and 3DOF closed-chain orientational manipulators, whose end-effector motion is actuated in a decoupled and homokinetic way by frame-located motors via holonomic transmissions based on constant-velocity couplings. The functioning of these couplings is investigated and the conditions applying for homokinetic transmission to be preserved during simultaneous motor drive are revealed and implemented. As a result, decoupled and configuration-independent relations between the motor rates and the time-derivatives of the variables describing the end-effector orientation are achieved. The attainment of analogous relations between the motor speeds and the components of the end-effector angular velocity is conversely proven to be unfeasible. The problem of singularities is furthermore examined, showing that input-output homokinesis is not a sufficient condition for a globally uniform kinetostatic behavior of the mechanism, which may, indeed, possibly reach uncertainty singular configurations. The connecting chains of the most typical constant-velocity couplings are analyzed, in order to obtain analytical expressions for the functions on which such singularities depend. The influence of design parameters is accordingly inspected. The results are valuable for the type and dimension synthesis of closed-chain wrists free from direct kinematic singularities, and characterized by simple kinematics and regular input-output kinetostatic relations.

Path Planning for Automated Robot Painting

2007 ◽  
Author(s):  
Finlay N. McPherson ◽  
Jonathan R. Corney ◽  
Raymond C. W. Sung
Keyword(s):  
Path Planning ◽  
Light Beam ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Kinematic Chain ◽  
Physical Contact ◽  
Kinematic Chains ◽  
Planning Algorithm ◽  
Rapid Prototyping And Manufacturing

This paper describes the analysis work underlying the path-planning algorithm for a robotic painting system. The system requires no bespoke production tooling and fills an automation gap in rapid prototyping and manufacturing technology that is currently occupied by hand painting. The system creates images by exposing individual pixels of a photographic coating with a robot-mounted laser. The painting process requires no physical contact so potentially images could be developed on any shape regardless of its complexity: As objects can only be “painted” when their surface can be “hit” (i.e. exposed) by the light beam the system requires six degrees of freedom to ensure all overhanging or reentrant areas can be exposed. The accuracy of serial robots degrades with the length of the kinematic chain (in other words six axis robots cannot position themselves with the same accuracy as four axis ones). Consequently to ensure high precision in the location and orientation of the light source, the object being exposed is mounted on a rotary tilt table within the workspace of a four-axis robot. This gives a six-degree of freedom positioning system composed of two separate kinematic chains. Although the resulting system is accurate the problems of constructing a coordinated path that allows the light beam to efficiently sweep (i.e. cover) the surface regardless of its geometry are challenging. This paper describes the difficulties and, after reviewing existing path planning algorithms, a new algorithm is introduced firstly by describing the nature of the system’s configuration space and then further developing this concept as an alternative to a previously described planning algorithm. Having outlined the approach the paper presents a kinematic model for the system and compares the configuration space approach to a purely Cartesian planning approach.

Singularity Analysis on a Special Class of Cable-Suspended Parallel Mechanisms With Pairwise Cable Arrangement and Actuation Redundancy

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Lewei Tang ◽  
Pengshuai Shi ◽  
Li Wu ◽  
Xiaoyu Wu ◽  
Xiaoqiang Tang
Keyword(s):  
Special Class ◽  
Degrees Of Freedom ◽  
Full Rank ◽  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Actuation Redundancy ◽  
Translational Movement ◽  
The Matrix ◽  
Redundant Actuators

Abstract This paper presents a singularity study on a special class of spatial cable-suspended parallel mechanisms (CSPMs) with merely three translational degrees of freedom using redundant actuators. This paper focuses on the CSPMs that have the capability to perform the purely translational movement with pairwise cables as parallelograms. There are two types of singularity to be discussed, which result from dynamic equations of CSPMs and the parallelogram constraint of pairwise cables. To ensure three-translational dofs without rotation of the end-effector, the matrix formed by normals of the planes based on each pairwise cables should maintain in full rank. In the case study, four typical designs of CSPMs with a planar end-effector and a spatial end-effector are discussed to clarify and conclude the singularity features of CSPMs with actuation redundancy. The results show that for some architectures there exist both types of singularity for redundantly actuated CSPMs with pairwise cables but for some other architectures the redundant actuation exerts no effect on the singularity issue.

A Parallelogram-Based Parallel Manipulator For Scho¨nflies Motion

2006 ◽  
Author(s):  
Oscar Salgado ◽  
Oscar Altuzarra ◽  
Enrique Amezua ◽  
Alfonso Herna´ndez
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
End Effector ◽  
Fixed Direction ◽  
Axis Parallel

A parallelogram-based four degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Scho¨nflies motion, that allows the end-effector to translate in all directions and rotate around an axis parallel to a fixed direction. The Theory of Group of Displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and a improved stiffness to the manipulator. The paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator and some technical applications in which the manipulator can be used are presented.

Real-Time Direct Position Analysis of Parallel Spherical Wrists by Using Extra Sensors

2005 ◽  
Vol 128 (1) ◽  
pp. 288-294 ◽  
Author(s):  
R. Vertechy ◽  
V. Parenti-Castelli
Keyword(s):  
Real Time ◽  
Measurement Errors ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
The Body ◽  
Least Square ◽  
End Effector ◽  
Kinematic Chains ◽  
Position Analysis ◽  
Specialized Form

The paper presents an algorithm for the real-time evaluation of the actual end-effector orientation of general parallel spherical wrists. Conceptually, the method relies on evidence that the pose of a rigid body is defined once the location of at least two linearly independent vectors attached to the body is known. The location of these vectors of the wrist end-effector is determined by the solution of the direct position analysis of some properly chosen kinematic chains (legs) of the manipulator. In order to accomplish this analysis, extra sensors, which measure suitable non-actuated variables of the chosen legs, need to be placed in addition to the ones normally embedded in the servomotors, i.e., the sensors which measure the actuated variables. From a mathematical point of view, the algorithm is built on the polar decomposition of a matrix and has inherent least square features. Thus, together with measurement redundancy, i.e., more sensors (extra sensors) than the mechanism degrees of freedom, the method also makes it possible to minimize the influence of both round-off and measurement errors on the estimation of the location of the wrist end-effector. The method is general but, in order to prove its effectiveness, without loss of generality it has been customized to the solution of the 3(UPS)-S fully parallel wrist architecture (where U, P and S are for universal, prismatic and spherical joint, respectively). Comparison of the proposed method, in both its general and specialized form, with others from the literature is provided.

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