Analytical Determination of Principal Twists and Singular Directions in Robot Manipulators

2003 ◽  
Author(s):  
Sandipan Bandyopadhyay ◽  
Ashitava Ghosal
Keyword(s):  
Degrees Of Freedom ◽  
Riemannian Metric ◽  
Degree Of Freedom ◽  
Body Motion ◽  
Inner Product ◽  
Analytical Determination ◽  
End Effector ◽  
Singular Configurations ◽  
Analytical Expressions

The identification of principal twists of the end-effector of a manipulator undergoing multi-degree-of-freedom motion is considered to be one of the central problems in kinematics. In this paper, we use dual velocity vectors to parameterize se(3), the space of twists, and define an inner product of two dual velocities as a dual number analog of a Riemannian metric on SE(3). We show that the principal twists can be obtained from the solution of an eigenvalue problem associated with this dual metric. It is shown that the computation of principal twists for any degree-of-freedom (DoF) of rigid-body motion, requires the solution of at most a cubic dual characteristic equation. Furthermore, the special nature of the coefficients yields simple analytical expressions for the roots of the dual cubic, and this in turn leads to compact analytical expressions for the principle twists. We also show that the method of computation allows us to separately identify the rotational and translational degrees-of-freedom lost or gained at singular configurations. The theory is applicable to serial, parallel, and hybrid manipulators, and is illustrated by obtaining the principal twists and singular directions for a 3-DoF parallel, and a hybrid 6-DoF manipulator.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems

2019 ◽  
Vol 24 (12) ◽  
pp. 3843-3861 ◽  
Author(s):  
Mario Lázaro
Keyword(s):  
Past History ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Critical Curves ◽  
History Of ◽  
Definition Of ◽  
Analytical Expressions ◽  
Critical Damping

In this paper, exact closed forms of critical damping manifolds for multiple-kernel-based nonviscous single-degree-of-freedom oscillators are derived. The dissipative forces are assumed to depend on the past history of the velocity response via hereditary exponential kernels. The damping model depends on several parameters, considered variables in the context of this paper. Those parameter combinations which establish thresholds between induced overdamped and underdamped motion are called critical damping manifolds. If such manifolds are represented on a coordinate plane of two damping parameters, then they are named critical curves, so that overdamped regions are bounded by them. Analytical expressions of critical curves are deduced in parametric form, considering certain local nondimensional parameters based on the Laplace variable in the frequency domain. The definition of the new parameter (called the critical parameter) is supported by several theoretical results. The proposed expressions are validated through numerical examples showing perfect fitting of the determined critical curves and overdamped regions.

A new parallel wrist using only revolute pairs: the 3-RUU wrist

Robotica ◽  
2001 ◽  
Vol 19 (3) ◽  
pp. 305-309 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Explicit Form ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Geometric Errors ◽  
End Effector ◽  
Singular Configurations ◽  
Overconstrained Mechanisms ◽  
Three Degrees Of Freedom

Only one parallel wrist with three equal legs containing just revolute pairs has been already presented in the literature. This parallel wrist is overconstrained, i.e., it involves three degrees of freedom required to orientate the end effector by using repetitions of constraints. The overconstrained mechanisms have the drawback of jamming or undergoing high internal loads when geometric errors occur. This paper presents a new parallel wrist, named 3-RUU wrist. The 3-RUU wrist is not overconstrained. It has three equal legs just involving revolute pairs and actuators adjacent to the frame and uses an architecture (3-RUU) already employed to obtain manipulators that make the end effector translate. The 3-RUU wrist kinematic analysis is addressed. This analysis shows that the new parallel wrist can reach singular configurations (translation singularities) in which the spherical constraint between end effector and frame fails. The singularity condition that makes finding all the 3-RUU wrist singular configurations possible is written in explicit form and geometrically interpreted.

scholarly journals Analysis of influence of circular hole on stress state of plate in pure bending condition

2021 ◽  
Vol 27 (1) ◽  
pp. 33-39
Author(s):  
Dragan Petrović ◽  
Milan Bižić
Keyword(s):  
Stress State ◽  
Circular Hole ◽  
Mathematical Formulation ◽  
Analytical Determination ◽  
Infinite Dimensions ◽  
Ansys Software ◽  
Pure Bending ◽  
Zone Of Influence ◽  
Analytical Expressions

The task of this paper is determining the zone of influence of a circular hole on the stress state of a homogeneous isotropic plate in pure bending condition. For solving the problem, the complex variable method was used which allows the complete analytical determination of the stresses at every point of the plate, and particularly on the contour of the circular hole. The analytical expressions for stresses in the plate of infinite dimensions were the basis for deriving a mathematical formulation which defines the zone as a function of diameter of the hole, inside which there is influence of the hole on the stress state of the plate. Obtained results are verified with FEM using the ANSYS software package whereby the input data for spatial discretization and mesh generation are not previously adjusted but was used a mesh that is generated automatically by the program.

Impedance Control of Space Robots Using Passive Degrees of Freedom in Controller Domain

2005 ◽  
Vol 127 (4) ◽  
pp. 564-578 ◽  
Author(s):  
Pushpraj Mani Pathak ◽  
Amalendu Mukherjee ◽  
Anirvan Dasgupta
Keyword(s):  
Force Control ◽  
Degrees Of Freedom ◽  
Impedance Control ◽  
Space Structure ◽  
Degree Of Freedom ◽  
Robotic Systems ◽  
Stable Method ◽  
Space Robots ◽  
End Effector ◽  
Control Schemes

Impedance control is an efficient and stable method of providing trajectory and force control in robotic systems. The procedure by which the impedance of the manipulator is changed is a very important aspect in the design of impedance based control schemes. In this work, a scheme is presented in which the control of impedance at the interface of the end effector and the space structure is achieved by introduction of a passive degree of freedom (DOF) in the controller of the robotic system. The impedance is shown to depend upon a compensation gain for the dynamics of the passive DOF. To illustrate the methodology, an example of a two DOF planer space robot is considered.

A 7R-Based, Two Degrees of Freedom Robomech

2000 ◽  
Author(s):  
Ahmad A. Smaili
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Architecture ◽  
Degree Of Freedom ◽  
Robot Arm ◽  
End Effector ◽  
Kinematic Constraints ◽  
Two Degrees Of Freedom ◽  
Synthesis Procedure ◽  
Two Degree Of Freedom

Abstract A robomech is a crossbreed of a mechanism and a robot arm. It has a parallel architecture equipped with more than one end effector to accomplish tasks that require the coordination of many functions. Robomechs with multi degrees of freedom that are based on the 4R and 5R chains have found their way into the literature. This article presents a new, two-degree of freedom robomech whose architecture is based on the 7R chain. The robomech is capable of performing two-function tasks. The features, kinematic constraints, and synthesis procedure of the robomech are outlined and an application example is given.

scholarly journals A discrete path/trajectory planner for robotic arms

1989 ◽  
Vol 31 (1) ◽  
pp. 1-28 ◽  
Author(s):  
H. H. Tan ◽  
R. B. Potts
Keyword(s):  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Challenging Problem ◽  
Final State ◽  
End Effector ◽  
Joint Torques ◽  
Robotic Arms ◽  
Joint Coordinates ◽  
Simulation Results

AbstractAn interesting and challenging problem in robotics is the off-line determination of the minimum cost path along which an end effector should move from a given initial to a given final state. This paper presents a discrete minimum cost path/trajectory planner which provides a general solution and allows for a range of constraints such as bounds on joint coordinates, joint velocities, joint torques and joint jerks. To demonstrate the practicability and feasibility of the planner, simulation results are presented for the Stanford manipulator using three and then the full six of its degrees of freedom. Simulation runs with two-link planar arms are also presented to enable a comparison with previously published results.

Two-Degree-of-Freedom Decoupled Nonredundant Cable-Loop-Driven Parallel Mechanism

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Hanwei Liu ◽  
Clément Gosselin ◽  
Thierry Laliberté
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
The Other ◽  
End Effector ◽  
Two Degrees Of Freedom ◽  
Actuation Redundancy ◽  
Rigid Link ◽  
Force Closure ◽  
Two Degree Of Freedom

A novel two-degree-of-freedom (DOF) cable-loop slider-driven parallel mechanism is introduced in this paper. The novelty of the mechanism lies in the fact that no passive rigid-link mechanism or springs are needed to support the end-effector (only cables are connected to the end-effector) while at the same time there is no actuation redundancy in the mechanism. Sliders located on the edges of the workspace are used and actuation redundancy is eliminated while providing force closure everywhere in the workspace. It is shown that the two degrees of freedom of the mechanism are decoupled and only two actuators are needed to control the motion. There are two cable loops for each direction of motion: one acts as the actuating loop while the other is the constraint loop. Due to the simple geometric design, the kinematic and static equations of the mechanism are very compact. The stiffness of the mechanism is also analyzed in the paper. It can be observed that the mechanism's stiffness is much higher than the stiffness of the cables. The proposed mechanism's workspace is essentially equal to its footprint and there are no singularities.

DETERMINATION OF THE ANALYTICAL WORKSPACE BOUNDARIES OF A NOVEL 2-DOF PLANAR TENSEGRITY MECHANISM

2010 ◽  
Vol 34 (1) ◽  
pp. 75-91 ◽  
Author(s):  
Marc Arsenault
Keyword(s):  
Weight Ratio ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Analytical Expressions ◽  
Two Degree Of Freedom ◽  
High Payload

Tensegrity mechanisms are slowly emerging as potential alternatives to more conventional mechanisms for certain types of applications where a reduced inertia of the mobile parts and a high payload to weight ratio are sought. With this in mind, a two-degree-of-freedom planar tensegrity mechanism is developed using a simple actuation strategy to keep the mechanism in self-stressed configurations. Solutions to the mechanism’s direct and inverse kinematic problems are first developed and are then used to determine analytical expressions for its workspace boundaries.

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