Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators

2004 ◽  
Vol 126 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Jing Wang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Special Class ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Parallel Mechanisms ◽  
Singular Configurations ◽  
Planning And Control ◽  
Robot Trajectory ◽  
Special Cases ◽  
And Control

In this paper, the singularity loci of a special class of spherical 3-DOF parallel manipulators with prismatic actuators are studied. Concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the expression of the determinant of the Jacobian matrix and the inverse kinematics of the manipulators. It is well known that there exist three different types of singularities for parallel manipulators, each having a different physical interpretation. In general, the singularity of type II is located inside the Cartesian workspace and leads to the instability of the end-effector. Therefore, it is important to be able to identify the configurations associated with this type of singularity and to find their locus in the space of all configurations. For the class of manipulators studied here, the six general cases and the five special cases of singularities are discussed. It is shown that the singularity loci in the Cartesian space (defined by the three Euler angles) are six independent planes. In the joint space (defined by the length of the three input links), the singularity loci are quadric surfaces, such as hyperboloid, sphere or a degenerated line or a degenerated circle. In addition, the three-dimensional graphical representations of the singular configurations in each of the general and special cases are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control.

Enumeration of Singular Configurations for Robotic Manipulators

1991 ◽  
Vol 113 (3) ◽  
pp. 272-279 ◽  
Author(s):  
H. Lipkin ◽  
E. Pohl
Keyword(s):  
Joint Angle ◽  
Robotic Manipulators ◽  
Systematic Procedure ◽  
Singular Configurations ◽  
Special Cases ◽  
Angle Space ◽  
Six Degree Of Freedom ◽  
Kinematic Singularities ◽  
And Control ◽  
Space Approach

Kinematic singularities are important considerations in the design and control of robotic manipulators. For six degree-of-freedom manipulators, the vanishing of the determinant of the Jacobian yields the conditions for the primary singularities. Examining the vanishing of the minors of the Jacobian yields further singularities which are special cases of the primary ones. A systematic procedure is presented to efficiently enumerate all possible singular configurations. Special geometries of representative manipulators are exploited by expressing the Jacobian in terms of vector elements. In contrast to using a joint-angle space approach, the resulting expressions yield direct physical interpretations.

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.

Complex Unconstrained Three-Dimensional Hand Movement and Constant Equi-Affine Speed

2009 ◽  
Vol 101 (2) ◽  
pp. 1002-1015 ◽  
Author(s):  
Uri Maoz ◽  
Alain Berthoz ◽  
Tamar Flash
Keyword(s):  
Power Law ◽  
Hand Movement ◽  
Three Dimensional ◽  
Hand Movements ◽  
Human Hand ◽  
Local Geometry ◽  
Planning And Control ◽  
Human Movements ◽  
And Control ◽  
Geometry And Kinematics

One long-established simplifying principle behind the large repertoire and high versatility of human hand movements is the two-thirds power law—an empirical law stating a relationship between local geometry and kinematics of human hand trajectories during planar curved movements. It was further generalized not only to various types of human movements, but also to motion perception and prediction, although it was unsuccessful in explaining unconstrained three-dimensional (3D) movements. Recently, movement obeying the power law was proved to be equivalent to moving with constant planar equi-affine speed. Generalizing such motion to 3D space—i.e., to movement at constant spatial equi-affine speed—predicts the emergence of a new power law, whose utility for describing spatial scribbling movements we have previously demonstrated. In this empirical investigation of the new power law, subjects repetitively traced six different 3D geometrical shapes with their hand. We show that the 3D power law explains the data consistently better than both the two-thirds power law and an additional power law that was previously suggested for spatial hand movements. We also found small yet systematic modifications of the power-law's exponents across the various shapes, which further scrutiny suggested to be correlated with global geometric factors of the traced shape. Nevertheless, averaging over all subjects and shapes, the power-law exponents are generally in accordance with constant spatial equi-affine speed. Taken together, our findings provide evidence for the potential role of non-Euclidean geometry in motion planning and control. Moreover, these results seem to imply a relationship between geometry and kinematics that is more complex than the simple local one stipulated by the two-thirds power law and similar models.

CARTESIAN APPROACH FOR GAIT PLANNING AND CONTROL OF BIPED ROBOTS ON IRREGULAR SURFACES

2009 ◽  
Vol 06 (04) ◽  
pp. 675-697 ◽  
Author(s):  
S. ALI A. MOOSAVIAN ◽  
MANSOOR ALGHOONEH ◽  
AMIR TAKHMAR
Keyword(s):  
Center Of Mass ◽  
Joint Space ◽  
Computational Effort ◽  
Simulation Studies ◽  
Pd Controller ◽  
Biped Robots ◽  
Gait Planning ◽  
Trunk Motion ◽  
Planning And Control ◽  
And Control

Biped robots possess higher capabilities than other mobile robots for moving on uneven environments. However, due to natural postural instability of these robots, their motion planning and control become a more important and challenging task. This article presents a Cartesian approach for gait planning and control of biped robots without the need to use the inverse kinematics and the joint space trajectories, thus the proposed approach could substantially reduce the processing time in both simulation studies and online implementations. It is based on constraining four main points of the robot in Cartesian space. This approach exploits the concept of Transpose Jacobian control as a virtual spring and damper between each of these points and the corresponding desired trajectory, which leads to overcome the redundancy problem. These four points include the tip of right and left foot, the hip joint, and the total center of mass (CM). Furthermore, in controlling biped robots based on desired trajectories in the task space, the system may track the desired trajectory while the knee is broken. This problem is solved here using a PD controller which will be called the Knee Stopper. Similarly, another PD controller is proposed as the Trunk Stopper to limit the trunk motion. Obtained simulation results show that the proposed Cartesian approach can be successfully used in tracking desired trajectories on various surfaces with lower computational effort.

scholarly journals Three-dimensional visualization of mission planning and control for the NPS autonomous underwater vehicle

1990 ◽  
Vol 15 (3) ◽  
pp. 217-221 ◽  
Author(s):  
M.J. Zyda ◽  
R.B. McGhee ◽  
S. Kwak ◽  
D.B. Nordman ◽  
R.C. Rogers ◽  
...  
Keyword(s):  
Autonomous Underwater Vehicle ◽  
Three Dimensional ◽  
Underwater Vehicle ◽  
Mission Planning ◽  
Planning And Control ◽  
And Control

Determination of singularity contours for five-bar planar parallel manipulators

Robotica ◽  
2000 ◽  
Vol 18 (5) ◽  
pp. 569-575 ◽  
Author(s):  
Gürsel Alıcı
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Point Of View ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Singular Configurations ◽  
Planning And Design ◽  
Prismatic Joints ◽  
Planar Parallel Manipulators

From a design point of view, it is crucial to predict singular configurations of a manipulator in terms of inputs in order to improve the dexterity and workspace of a manipulator. In this paper, we present a simple, yet a systematic appoach to obtain singularity contours for a class of five-bar planar parallel manipulators which are based on five rigid links and five single degree of freedom joints – revolute and prismatic joints. The determinants of the manipulator Jacobian matrices are evaluated in terms of joint inputs for a specified set of geometric parameters, and the contours of the determinants at 0.0 plane which are the singularity contours in joint space are generated for the three types of singularities reported in the literature. The proposed approach/algorithm is simple and systematic, and the resulting equations are easy to solve on a computer. The singularity contours for all the class are presented in order to demonstrate the method. It is concluded that the proposed method is useful in trajectory planning and design of five-bar planar parallel manipulators in order to improve their dexterity and workspace.

Planning and control of three-dimensional multi-agent formations

2012 ◽  
Vol 30 (2) ◽  
pp. 265-284 ◽  
Author(s):  
G. Wen ◽  
Z. Peng ◽  
Y. Yu ◽  
A. Rahmani
Keyword(s):  
Three Dimensional ◽  
Planning And Control ◽  
Multi Agent ◽  
And Control

Structure Synthesis of a Class of Parallel Manipulators with Fully Decoupled Projective Motion

2021 ◽  
pp. 1-17
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Special Class ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Parallel Manipulators ◽  
Joint Space ◽  
End Effector ◽  
Geometrical Reasoning ◽  
Structure Synthesis ◽  
Decoupled Motion ◽  
One To One

Abstract This paper describes the structure synthesis of a special class of parallel manipulators with fully decoupled motion, that is, a one-to-one correspondence between the instantaneous motion space of the end-effector and the joint space of the manipulator. A notable finding of this study is that a fully decoupled design can be achieved for parallel manipulators with any number of degrees of freedom (DOFs) when the rotational DOF of the end-effector is expressed in the form of a projective angle representation. On the basis of the geometrical reasoning of the projective motion interpreted by screw algebra, a systematic approach is developed for synthesizing the structures of f-DOF (f ≤ 6) parallel manipulators with fully decoupled projective motion. Several 2-, 3-, 4-, 5-, and 6-DOF parallel manipulators with fully decoupled projective motion were designed for illustrating the developed method.

scholarly journals SINGULARITY ANALYSIS OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

1970 ◽  
Vol 41 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Motion Control ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Redundant Manipulators ◽  
Static Behavior ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
And Control ◽  
Planar Parallel Manipulators

Finding Singular configurations (singularities) is one of the mandatory steps during the design and control of mechanisms. Because, in these configurations, the instantaneous kinematics is locally undetermined that causes serious problems both to static behavior and to motion control of the mechanism. This paper addresses the problem of determining singularities of a 3-PRRR kinematically redundant planar parallel manipulator by use of an analytic technique. The technique leads to an input –output relationship that can be used to find all types of singularities occurring in this type of manipulators.Key Words: Planar parallel manipulators; Redundant manipulators; Singularity analysis; Jacobian matrices.DOI: 10.3329/jme.v41i1.5356Journal of Mechanical Engineering, Vol. ME 41, No. 1, June 2010 1-6

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