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Geometric algebra approach to analyzing the singularity of six-DOF parallel mechanism

Shili CHENG, Ping JI
2019 Journal of Advanced Mechanical Design, Systems, and Manufacturing  
This paper presents an approach of singularities analysis of six degrees of freedom (DOF) parallel mechanism applying geometric algebra.  ...  Singular configurations must be avoided in the practical manipulation of parallel mechanism.  ...  BK20140470) and Talents Introduction Project of Yancheng Institute of Technology of China (Grant No. KJC2013016).  ... 
doi:10.1299/jamdsm.2019jamdsm0076 fatcat:hnr4hpi7ajcztg3mhr4nkeu5ca

Matrix modeling of inverse dynamics of spatial and planar parallel robots

Stefan Staicu
2011 Multibody system dynamics  
The study of the dynamics of the parallel mechanisms is done mainly to solve successfully the control of the motion of such robotic systems.  ...  For the same evolution of the moving platform, the power distribution upon the three actuators depends on the actuating configuration, but the total power absorbed by the set of three actuators is the  ...  Angeles [9] , Wang and Gosselin [10] , Staicu [11] analyzed the kinematics, dynamics and singularity loci of Agile Wrist spherical robot with three actuators.  ... 
doi:10.1007/s11044-011-9281-8 fatcat:sashclvjqvftzatbj2nrcvwism

Structure and Property of the Singularity Loci of Gough-Stewart Manipulator [chapter]

Yi Cao, Yanwen Li, Zhen Huang
2010 Advanced Strategies for Robot Manipulators  
Gosselin (1994, 1995) studied singularity loci of planar and spherical parallel mechanisms.  ...  The singularity equation for this orientation is a special irresolvable polynomial expression of degree three, and the structure of the singularity loci in infinite parallel principal sections includes  ...  Structure and Property of the Singularity Loci of Gough-Stewart Manipulator, Advanced Strategies for Robot Manipulators, S.  ... 
doi:10.5772/10204 fatcat:7yp5czsj4vdjbmzs4uyguyyrvm

Self-Motions of General 3-RPR Planar Parallel Robots

Sébastien Briot, Vigen Arakelian, Ilian A. Bonev, Damien Chablat, Philippe Wenger
2008 The international journal of robotics research  
Special cases of self-motions are then examined and the degree of freedom gained in such special configurations is kinematically interpreted.  ...  This paper studies the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints.  ...  For example, in , it is shown that all singularities of the special 3-RRR (R stands for a passive revolute joint, and R for an actuated revolute joint) spherical parallel robot, known as the Agile Eye,  ... 
doi:10.1177/0278364908092466 fatcat:3irtgcgosjeqpbtxpzdsqf3oiy

A New Concept Compliant Platform with Spatial Mobility and Remote Actuation

Nicola Pio Belfiore
2019 Applied Sciences  
The presented platform makes use of lumped compliance with three different kinds of elastic joints.  ...  An analysis of the platform mobility based on finite element analysis is provided together with an assembly mode analysis of the equivalent pseudo-rigid body mechanism.  ...  Topological Analysis Considering an equivalent mechanism PRBM with rigid bodies and classical U, S, and R pairs, three legs guarantee six degrees of freedom to the platform.  ... 
doi:10.3390/app9193966 fatcat:ct3u3lormjhkhdcxlkh2ho3e7m

Comparison of 3-[PP]S Parallel Manipulators based on their Singularity Free Orientation Workspace, Parasitic Motions and Complexity

Abhilash Nayak, Stéphane Caro, Philippe Wenger
2018 Mechanism and Machine Theory  
Hence, this paper attempts to compare a class of 3 degreeof-freedom parallel manipulators belonging to the 3-[PP]S family, for which each leg is confined to move in a plane with the first two joints generating  ...  The choice of a parallel manipulator for a particular application is a challenging task due to the existence of numerous designs that generate the same motion type.  ...  Acknowledgments This work was conducted with the support of both Centrale Nantes and the French National Research Agency (ANR project Kapamat #ANR-14-CE34-0008-01).  ... 
doi:10.1016/j.mechmachtheory.2018.08.001 fatcat:p5ke5lnwlbas7b2qycyizp7heq

Modelling of a special class of spherical parallel manipulators with Euler parameters

Shaoping Bai, Michael R. Hansen, Torben O. Andersen
2008 Robotica (Cambridge. Print)  
A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper.  ...  Moreover, a homogeneous workspace can be obtained with Euler parameters for the SPMs, which facilitates the evaluation of dexterity.  ...  The modelling work is carried out for a special class of spherical parallel manipulators, which have a symmetrical architecture with identical legs.  ... 
doi:10.1017/s0263574708004402 fatcat:g5r6lf43djabrbv7a66zv7iyea

Topological Methods for Singularity-Free Path-Planning [chapter]

Davide Paganelli
2010 Robot Manipulators Trends and Development  
Fortunately, the critical points where 0 c p J J   are all singular, and must be ruled out of the analysis.  ...  It is devoted for a large scale of applications, such as manufacturing, manipulation, medicine and automation.  ...  The developed method will be applied to three classes of parallel manipulators with three degrees of freedom, and numerical examples will show its effectiveness.  ... 
doi:10.5772/9208 fatcat:pg2b7iou4zfvnj3qgqcgl3ef3a

Inverse dynamics of a 3-PRC parallel kinematic machine

Yangmin Li, Stefan Staicu
2011 Nonlinear dynamics  
Recursive matrix relations for kinematics and dynamics analysis of a three-prismatic-revolutecylindrical (3-PRC) parallel kinematic machine (PKM) are performed in this paper.  ...  Finally, compact matrix equations and graphs of simulation for input force and power of each of three actuators are obtained.  ...  Angeles [9] , Wang and Gosselin [10] , Staicu [11] analysed the kinematics, dynamics and singularity loci of Agile Wrist spherical robot with three actuators.  ... 
doi:10.1007/s11071-011-0045-z fatcat:6yjhosbfvrhrznxnv572wpfd2e

Kinematic Singularities of Robot Manipulators [chapter]

Peter Donelan
2010 Advances in Robot Manipulators  
and three types having higher degree of freedom: cylindrical C with 2 dof, planar E and spherical S each with 3 dof.  ...  These include three types with one degree of freedom (dof): revolute R, prismatic P and helical or screw H (the first two correspond to purely rotational and purely translational freedom respectively)  ...  /kinematic-singularities-of-robot-manipulators  ... 
doi:10.5772/9548 fatcat:un6d3sajebbj3ouv52pd4savti

Determination of Singularities in Delta-Like Manipulators

Raffaele Di Gregorio
2004 The international journal of robotics research  
The DELTA robot and the manipulators derived from the DELTA robot are a relevant class of translational manipulators.  ...  In this paper, the mobility analysis of these parallel translational manipulators is developed in full.  ...  Acknowledgment The financial support of the Italian MURST is gratefully acknowledged.  ... 
doi:10.1177/0278364904039689 fatcat:ipsrgjnw65gj3mrdp2gier42uu

Flagged Parallel Manipulators

M. Alberich-Carraminana, F. Thomas, C. Torras, C. Torras
2007 IEEE Transactions on robotics  
The main interest of flagged parallel manipulators is that their singularity loci admit a well-behaved decomposition with a unique topology irrespective of the metrics of each particular design.  ...  The conditions for a parallel manipulator to be flagged can be simply expressed in terms of linear dependencies between the coordinates of its leg attachments, both on the base and on the platform.  ...  In a singular configuration, the mechanism gains some degrees-of-freedom (DOF) and becomes uncontrollable.  ... 
doi:10.1109/tro.2007.903819 fatcat:exygzhzi7zetfd5axcnx4odrtq

A Novel 4-DOF Parallel Manipulator H4 [chapter]

Jinbo Wu, Zhouping Yi
2008 Parallel Manipulators, towards New Applications  
degrees of freedom.  ...  A parallel manipulator has a singular position if the axes of its hydraulic cylindrical legs lie in a linear complex, a special three-parameter set of lines.  ...  This is a singular configuration.  ... 
doi:10.5772/5441 fatcat:kpmp26rhbvbqtnoxqy2tqhaiym

Conditions for line-based singularities in spatial platform manipulators

Fangli Hao, J. Michael McCarthy
1998 Journal of Robotic Systems  
A geometric classification of these "line-based" singularities is presented.  ...  In this paper, we consider singular configurations of manipulator systems that can be modeled as a platform supported by serial robotic chains.  ...  Acknowledgements The insight and advice of Curtis Collins (UCI) and Gregory Long (Reflex Technologies, Inc.) are gratefully acknowledged.  ... 
doi:10.1002/(sici)1097-4563(199812)15:1<43::aid-rob4>;2-s fatcat:sv36sr2ylnaepgstj6clur6kma

Singularity-theoretic methods in robot kinematics

P. S. Donelan
2007 Robotica (Cambridge. Print)  
The first three links determine a positioning sub-assembly (regional manipulator) while the last three form a spherical wrist sub-assembly.  ...  with singularities of the position of the wrist centre (det J 12 = 0).  ...  on the degrees of freedom of its individual actuated joints, subject to constraints such as closed loops.  ... 
doi:10.1017/s0263574707003748 fatcat:2muiwcxyeve3je5ktuyn435gci
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