Example of Internal Redundancy to Improve the Dynamics Performance of Parallel Manipulators

2012 ◽  
Author(s):  
Soheil S. Parsa ◽  
Juan A. Carretero ◽  
Roger Boudreau
Keyword(s):  
Dynamic Model ◽  
Dynamic Properties ◽  
Center Of Mass ◽  
Parallel Manipulators ◽  
Redundant Manipulators ◽  
Serial Manipulators ◽  
Numerical Example ◽  
Kinematic Singularities ◽  
First Time

In recent years, redundancy in parallel manipulators has been discussed for the cases of kinematic, actuation and branch redundancy. Some advantages of these redundant manipulators include the reduction or elimination of some types of kinematic singularities and/or an increase of their reachable and dexterous workspaces, to name a few. Internal redundancy, first introduced for serial manipulators, refers to the concept of adding movable masses to some links so as to allow to control the center of mass and other dynamic properties of some links. In this paper, the concept of internal redundancy is investigated for the first time in the context of parallel manipulators. More specifically, the 3-RRR planar manipulator, where a movable mass has been added to the distal link, is analysed. The manipulator’s dynamic model is briefly introduced and then is used to track a simple trajectory. A numerical example is shown to support the idea.

Singularity robust balancing of parallel manipulators following inconsistent trajectories

Robotica ◽  
2014 ◽  
Vol 34 (9) ◽  
pp. 2027-2038 ◽  
Author(s):  
Mustafa Özdemir
Keyword(s):  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Type I ◽  
Type Ii ◽  
Inverse Dynamic ◽  
Serial Manipulators ◽  
Dynamic Solution ◽  
Singular Configuration ◽  
Kinematic Singularities

SUMMARYWhen compared to serial manipulators, parallel manipulators have small workspaces mainly due to their closed-loop structure. As opposed to type I singularities (or inverse kinematic singularities) that are generally encountered at the workspace boundaries, type II singularities characteristically arise within the workspace, and around them, the inverse dynamic solution becomes unbounded. Hence, a desired trajectory passing through a type II singular position cannot be achieved by the manipulator, and its useful workspace becomes further and substantially reduced. It has been previously shown in the literature that if the trajectory is replanned in such a way that the dynamic equations of motion of the manipulator are consistent at a type II singularity, i.e. if the trajectory is consistent, then the manipulator passes through this singular configuration in a controllable manner, while the inverse dynamic solution remains finite. An inconsistent trajectory, on the other hand, is stated in the literature to be unrealizable. However, although seems a promising technique, trajectory replanning itself is also a deviation from the originally desired trajectory, and there might be cases in applications where, due to some task-specific reasons, the desired trajectory, although inconsistent, is not allowed to be replanned to satisfy the consistency conditions. In this paper, a method of singularity robust balancing is proposed for parallel manipulators passing through type II singular configurations while following inconsistent trajectories. By this means, an originally unrealizable inconsistent trajectory passing through a type II singularity can be followed without any deviation, while the required actuator forces remain bounded after the manipulator is balanced according to the design methodology presented in this study. The effectiveness of the introduced method is shown through numerical simulations considering a planar 3-DOF 2-PRR parallel manipulator under different balancing scenarios.

scholarly journals Internal redundancy: an approach to improve the dynamic parameters around sharp corners

2013 ◽  
Vol 4 (1) ◽  
pp. 233-242 ◽  
Author(s):  
S. S. Parsa ◽  
J. A. Carretero ◽  
R. Boudreau
Keyword(s):  
Parallel Manipulator ◽  
Dynamic Properties ◽  
Dynamic Performance ◽  
Parallel Manipulators ◽  
Variable Geometry ◽  
Centre Of Mass ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
Sharp Corners

Abstract. In recent years, redundancy in parallel manipulators has been studied broadly due to its capability of overcoming some of the drawbacks of parallel manipulators including small workspaces and singular configurations. Internal redundancy, first introduced for serial manipulators, refers to the concept of adding movable masses to some links so as to allow to control the location of the centre of mass and other dynamic properties of some links. This concept has also been referred to as variable geometry. This paper investigates the effects of internal redundancy on the dynamic properties of a planar parallel manipulator while performing a family of trajectories. More specifically, the 3-RRR planar manipulator, where a movable mass has been added to the distal link, is allowed to trace trajectories with rounded corners and different radii. The proposed method uses the manipulator's dynamic model to actively optimise the location of the redundant masses at every point along the trajectory to improve the dynamic performance of the manipulator. Numerical examples are shown to support the idea.

DIRECT KINEMATIC ANALYSIS OF A FAMILY OF 4-DOF PARALLEL MANIPULATORS WITH A PASSIVE CONSTRAINING LEG

2011 ◽  
Vol 35 (3) ◽  
pp. 437-459 ◽  
Author(s):  
Soheil Zarkandi ◽  
Hamid R. Mohammadi Daniali
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Numerical Example ◽  
Fixed Base ◽  
Univariate Polynomials ◽  
Movable Platform ◽  
Univariate Polynomial ◽  
Kinematic Singularities

This paper presents direct kinematic analysis of a family of 3R1T parallel manipulators, while R and T denote the rotational and translational degrees of freedom respectively. The manipulators consist of two rigid bodies, a movable platform and a fixed (base) connected to each other by four active legs and one constraining passive leg. First, the direct position kinematics of the manipulators is analyzed. For a general manipulator of this class, this analysis results in a univariate polynomial of degree 30 along with a set of other univariate polynomials of degree 16 and 4 respectively. However, for a special architecture of the manipulators, it is shown that the direct position kinematics leads to a minimal univariate polynomial of degree 12. A numerical example is also included to confirm the results. Moreover, direct velocity and direct kinematic singularities of the manipulators are analyzed using Jacobian matrices.

scholarly journals Mass and spin for classical strings in dS3

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Klaas Parmentier
Keyword(s):  
Black Hole ◽  
Evolution Equation ◽  
Cosmic Strings ◽  
Center Of Mass ◽  
Open String ◽  
Conserved Quantities ◽  
Numerical Example ◽  
All Solutions

Abstract We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS3 static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser’s algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin < 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.

scholarly journals Structural Transitions at Microtubule Ends Correlate with Their Dynamic Properties in Xenopus Egg Extracts

2000 ◽  
Vol 149 (4) ◽  
pp. 767-774 ◽  
Author(s):  
Isabelle Arnal ◽  
Eric Karsenti ◽  
Anthony A. Hyman
Keyword(s):  
Dynamic Instability ◽  
Dynamic Properties ◽  
Microtubule Assembly ◽  
Two Dimensional ◽  
Egg Extracts ◽  
Xenopus Egg ◽  
Xenopus Egg Extracts ◽  
First Time ◽  
The Relationship ◽  
Dynamic Populations

Microtubules are dynamically unstable polymers that interconvert stochastically between growing and shrinking states by the addition and loss of subunits from their ends. However, there is little experimental data on the relationship between microtubule end structure and the regulation of dynamic instability. To investigate this relationship, we have modulated dynamic instability in Xenopus egg extracts by adding a catastrophe-promoting factor, Op18/stathmin. Using electron cryomicroscopy, we find that microtubules in cytoplasmic extracts grow by the extension of a two- dimensional sheet of protofilaments, which later closes into a tube. Increasing the catastrophe frequency by the addition of Op18/stathmin decreases both the length and frequency of the occurrence of sheets and increases the number of frayed ends. Interestingly, we also find that more dynamic populations contain more blunt ends, suggesting that these are a metastable intermediate between shrinking and growing microtubules. Our results demonstrate for the first time that microtubule assembly in physiological conditions is a two-dimensional process, and they suggest that the two-dimensional sheets stabilize microtubules against catastrophes. We present a model in which the frequency of catastrophes is directly correlated with the structural state of microtubule ends.

Wrench capabilities of planar parallel manipulators. Part I: Wrench polytopes and performance indices

Robotica ◽  
2008 ◽  
Vol 26 (6) ◽  
pp. 791-802 ◽  
Author(s):  
Flavio Firmani ◽  
Alp Zibil ◽  
Scott B. Nokleby ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Linear Mapping ◽  
Redundant Manipulators ◽  
Task Space ◽  
Performance Indices ◽  
Study Case ◽  
And Performance ◽  
Planar Parallel Manipulators

SUMMARYThis paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.

scholarly journals Study of the process $$e^+e^- \rightarrow \eta \pi ^0\gamma $$ in the energy range $$\sqrt{s} = {1.05-2.00}$$ GeV with the SND detector

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
M. N. Achasov ◽  
A. Yu. Barnyakov ◽  
A. A. Baykov ◽  
K. I. Beloborodov ◽  
A. V. Berdyugin ◽  
...  
Keyword(s):  
Energy Range ◽  
Cross Section ◽  
Center Of Mass ◽  
Wide Energy Range ◽  
Mass Energy ◽  
Center Of Mass Energy ◽  
Wide Energy ◽  
Radiation Processes ◽  
Using Data ◽  
First Time

AbstractThe process $$e^+e^-\rightarrow \eta \pi ^0\gamma $$ e + e - → η π 0 γ is studied in the center-of-mass energy range 1.05–2.00 GeV using data with an integrated luminosity of 94.5 $$\hbox {pb}^{-1}$$ pb - 1 collected by the SND detector at the VEPP-2000 $$e^{+}e^{-}$$ e + e - collider. The $$e^+e^-\rightarrow \eta \pi ^0\gamma $$ e + e - → η π 0 γ cross section is measured for the first time. It is shown that the dominant mechanism of this reaction is the transition through the $$\omega \eta $$ ω η intermediate state. The measured cross section of the subprocess $$e^+e^-\rightarrow \omega \eta \rightarrow \eta \pi ^0\gamma $$ e + e - → ω η → η π 0 γ is consistent with previous measurements in the $$e^+e^-\rightarrow \pi ^+\pi ^-\pi ^0\eta $$ e + e - → π + π - π 0 η mode. It is found, with a significance of $$5.6\sigma $$ 5.6 σ , that the process $$e^+e^-\rightarrow \eta \pi ^0\gamma $$ e + e - → η π 0 γ is not completely described by hadronic vector-pseudoscalar intermediate states. The cross section of this missing contribution, which can originate from radiation processes, e. g. $$e^+e^-\rightarrow a_{0}(1450)\gamma $$ e + e - → a 0 ( 1450 ) γ , is measured. It is found to be 15–20 pb in the wide energy range from 1.3 to 1.9 GeV.

Novel Precision PZT-Driven Micropositioning Stage with Large Travel Range

2009 ◽  
Vol 407-408 ◽  
pp. 159-162
Author(s):  
Hua Wei Chen ◽  
Ichiro Hagiwara
Keyword(s):  
Dynamic Model ◽  
Piezoelectric Actuator ◽  
Dynamic Properties ◽  
Flexure Hinge ◽  
Slip Model ◽  
Stick Slip ◽  
Friction Effect ◽  
Simulation Results

One novel long-travel piezoelectric-driven linear micropositioning stage capable of moving in a stepping mode is developed. The stick-slip friction effect between flexure hinge actuation tips with a sliding stage is used to drive the stage step-by-step through an enlarged displacement of piezoelectric actuator. In order to enlarge the travel range, magnifying mechanism is optimally designed by use of flexure hinge and lever beam. Moreover, dynamic model of such stage is proposed by consideration of reset integrator stick-slip model. The simulation results show that the stage has considerable good dynamic properties.

Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory1

2004 ◽  
Vol 126 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
General Procedure ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Validity Condition ◽  
First Time ◽  
Spherical Parallel Manipulator ◽  
Selection Of

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time.

Sign in / Sign up

Export Citation Format

Share Document