# Equimomental systems and robot dynamics

Conference item

Selig, JM (2015). Equimomental systems and robot dynamics.

*IMA Conference on Mathematics of Robotics.*St Anne’s College, University of Oxford 09 - 11 Sep 2015 London South Bank University. pp. ? - ? (8)

Authors | Selig, JM |
---|---|

Abstract | Three different concepts from the past are reviewed from a more modern standpoint. Constructing an equimomental system of four point-masses to an arbitrary rigid-body; the conditions for the generalised mass matrix of a serial robot to be constant and how to dynamically balance an arbitrary rigid body so that it is symmetrical about a given axis. Connections are made to the geometry of a 3-dimensional Veronese variety. |

Year | 2015 |

Publisher | London South Bank University |

Accepted author manuscript | License CC BY 4.0 File description Paper |

File | License CC BY 4.0 File description Presentation |

Publication dates | |

Print | 11 Sep 2015 |

Publication process dates | |

Deposited | 08 Jun 2017 |

Accepted | 11 Sep 2015 |

ISBN | 978-0-90-509133-4 |

Page range | ? - ? (8) |

Permalink -

https://openresearch.lsbu.ac.uk/item/875zz

##### 0

total views##### 5

total downloads##### 0

views this month##### 5

downloads this month

## Related outputs

##### On the Dynamics of a Ball Rolling on a Tipping Plane

Laus, LP and Selig, JM (2019). On the Dynamics of a Ball Rolling on a Tipping Plane.*15th IFToMM World Congress,.*Krakov, Poland, 30 Jun - 04 Jul 2019

##### Parallel Robots with Homokinetic Joints: The Zero-Torsion Case

Wu, Y, Selig, J and Carricato, M (2019). Parallel Robots with Homokinetic Joints: The Zero-Torsion Case.*15th IFToMM World Congress.*Krakov, Poland 30 Jun - 04 Jul 2019

##### Double Bennett Mechanisms with Assembly Modes of Different Dimensions

Selig, JM and Li, Z (2018). Double Bennett Mechanisms with Assembly Modes of Different Dimensions.*4th International Conference on Reconfigurable Mechanisms and Robots.*Delft 20 - 22 Jun 2018 London South Bank University.

##### Displacement Varieties for Some PUP Linkages

Selig, JM (2018). Displacement Varieties for Some PUP Linkages.*16th International Symposium on Advances in Robot Kinematics.*Bologna, Italy 01 - 05 Jul 2018

##### Hyperbolic pseudoinverses for kinematics in the Euclidean group

Selig, JM (2017). Hyperbolic pseudoinverses for kinematics in the Euclidean group.*SIAM Journal on Matrix Analysis and Applications.*38 (4), pp. 1541-1559.

##### Some rational vehicle motions

Selig, JM (2013). Some rational vehicle motions.*6th International Workshop on Computational Kinematics (CK2013).*Barcelona, Spain 12 - 15 May 2013 London South Bank University. doi:10.1007/978-94-007-7214-4-3

##### Manipulating robots along helical trajectories

Selig, JM and Ovseevitch, AI (2009). Manipulating robots along helical trajectories.*Robotica.*14 (3), pp. 261-267.

##### Motion Interpolation in Lie Subgroups and Symmetric Subspaces

Selig, JM, Wu, Y and Carricato, M (2017). Motion Interpolation in Lie Subgroups and Symmetric Subspaces.*7th IFToMM International Workshop of Computational Kinematics.*Futurescope, Poitiers, France 22 - 24 May 2017 London South Bank University. doi:http://doi.org/10.1007/978-3-319-60867-9_53

##### Some Remarks on the RRR Linkage

Selig, JM (2014). Some Remarks on the RRR Linkage. in: Lenarcic, J and Khatib, O (ed.) Advances in robot kinematics: analysis and design Switzerland Springer International Publishing. pp. 77 - 85 (9)##### Some Mobile Overconstrained Parallel Mechanisms

Selig, JM (2016). Some Mobile Overconstrained Parallel Mechanisms.*Advances in Robot Kinematics.*Grasse, France 27 - 30 Jun 2016 London South Bank University.

##### The complex of lines from successive points and the horopter

Selig, JM (2008). The complex of lines from successive points and the horopter.*IEEE International Conference on Robotics and Automation.*California 19 - 23 May 2008 London South Bank University. pp. 2380 - 2385 doi:10.1109/ROBOT.2008.4543569

##### A screw theory of static beams

Selig, JM and Ding, X (2001). A screw theory of static beams.*IEEE International Conference on Intelligent Robots and Systems.*San Diego, CA, USA 29 Oct - 03 Nov 2001 London South Bank University. doi:10.1109/IROS.2001.973376

##### Mobile Icosapods

Gallet, M, Nawratil, G, Schicho, J and Selig, JM (2017). Mobile Icosapods.*Advances in Applied Mathematics.*88 (July), pp. 1-25.

##### Note on the Principle of Transference

Selig, JM (1986). Note on the Principle of Transference.*Design Engineering Technical Conference.*Columbus, Ohio London South Bank University.

##### Scaling Direct Drive Robots

Wallace, R and Selig, JM (1995). Scaling Direct Drive Robots.*Robotics and Automation, 1995 IEEE International Conference on.*Nagoya, Japan 21 - 27 May 1995 Wallace.

##### Clifford algebra of points, lines and planes

Selig, JM (1999).*Clifford algebra of points, lines and planes.*London South Bank University School of Computing, Infromations Systems and Mathematics, South Bank University, London.

##### Some remarks on the statistics of pose estimation

Selig, JM (2000).*Some remarks on the statistics of pose estimation.*School of Computing, Information Systems and Mathematics, South Bank University, London.

##### Spatial stiffness matrix from simple stretched springs

Selig, JM (2000). Spatial stiffness matrix from simple stretched springs.*IEEE International Conference on Robotics & Automation.*San Francisco Ca. USA 24 - 28 Apr 2000 London South Bank University. doi:10.1109/ROBOT.2000.845218

##### Some mathematical problems in robotics

Selig, JM (2000).*Some mathematical problems in robotics.*School of Computing, Information Systems and Mathematics, South Bank University, London.

##### Theory of vibrations in Stewart platforms

Selig, JM and Ding, X (2001). Theory of vibrations in Stewart platforms.*IEEE International Conference on Intelligent Robots and Systems.*San Diego, CA USA London South Bank University. doi:10.1109/IROS.2001.976395

##### Interpolated rigid-body motions and robotics

Selig, JM and Yuanqing, W (2006). Interpolated rigid-body motions and robotics.*Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.*Beijing, China 09 - 15 Oct 2006 London South Bank University. pp. 1086 - 1091 doi:10.1109/IROS.2006.281815

##### Introduction to Polynomial Invariants of Screw Systems

Donelan, P and Selig, JM (2007).*Introduction to Polynomial Invariants of Screw Systems.*arXiv.

##### Clifford algebra of points, lines and planes

Selig, JM (2000). Clifford algebra of points, lines and planes.*Robotica.*18 (5), pp. 545 - 556.

##### Centrodes and Lie algebra

Selig, JM (2007). Centrodes and Lie algebra.*2th IFT oMM World Congress.*Besancon France 18 - 21 Jun 2007 London South Bank University. pp. ? - ? (6)

##### Cayley maps for SE(3)

Selig, JM (2007). Cayley maps for SE(3).*12th International Federation for the Promotion of Mechanism and Machine Science World Congress.*Besancon France London South Bank University. pp. ? - ? (6)

##### A geometric Newton-Raphson method for Gough-Stewart platforms

Selig, JM and Li, H (2009). A geometric Newton-Raphson method for Gough-Stewart platforms.*Fifth International Workshop on Computational Kinematics.*University of Duisburg-Essen, Germany 06 - 08 May 2009 London South Bank University. pp. 183 - 190 doi:10.1007/978-3-642-01947-0_23

##### Some rigid-body constraint varieties generated by linkages

Selig, JM (2012). Some rigid-body constraint varieties generated by linkages. in: Lenarcic, J and Husty, M (ed.) Latest Advances in Robot Kinematics Dordrecht Springer.##### A screw syzygy with applications to robot singularity computation

Selig, JM and Donelan, P (2008). A screw syzygy with applications to robot singularity computation. in: Advances in Robot Kinematics: Analysis and Design Netherlands Springer Science+Business Media B.V. pp. 147 - 154##### Dynamics of vibratory bowl feeders

Selig, JM and Dai, JS (2005). Dynamics of vibratory bowl feeders.*Proceedings of the 2005 IEEE International Conference on Robotics and Automation April 2005.*Barcelona, Spain Apr 2005 London South Bank University. doi:10.1109/ROBOT.2005.1570617

##### Active versus passive transformations in robotics

Selig, JM (2006). Active versus passive transformations in robotics.*IEEE Robotics and Automation Magazine.*13 (1), pp. 79 - 84.

##### Structure of the spatial stiffness matrix

Selig, JM and Ding, X (2002). Structure of the spatial stiffness matrix.*International Journal of Robotics and Automation.*17 (1), pp. 1 - 16.

##### Diagonal spatial stiffness matrices

Selig, JM and Ding, X (2002). Diagonal spatial stiffness matrices.*International Journal of Robotics and Automation.*17 (2), pp. 100 - 106.

##### Three problems in robotics

Selig, JM (2002). Three problems in robotics.*Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball.*University of Cambridge 09 - 11 Jul 2000 London South Bank University. doi:10.1243/0954406021524927

##### Exponential and cayley maps for dual quaternions

Selig, JM (2010). Exponential and cayley maps for dual quaternions.*Advances in Applied Clifford Algebras.*20 (3-4), pp. 923 - 936.

##### Half-turns and line symmetric motions

Selig, JM and Husty, M (2011). Half-turns and line symmetric motions.*Mechanism and Machine Theory.*46 (2), pp. 156 - 167.

##### On the instantaneous acceleration of points in a rigid body

Selig, JM (2011). On the instantaneous acceleration of points in a rigid body.*Mechanism and Machine Theory.*46 (10), pp. 1522 - 1535.

##### On the geometry of point-plane constraints on rigid-body displacements

Selig, JM (2011). On the geometry of point-plane constraints on rigid-body displacements.*Acta Applicandae Mathematicae.*116 (2), pp. 133 - 155.

##### Characterisation of Frenet-Serret and Bishop motions with applications to needle steering

Selig, JM (2013). Characterisation of Frenet-Serret and Bishop motions with applications to needle steering.*Robotica.*31 (6), pp. 981 - 992.

##### On the compliance of coiled springs

Ding, X and Selig, JM (2004). On the compliance of coiled springs.*International Journal of Mechanical Sciences.*46 (5), pp. 703 - 727.

##### Curves of stationary acceleration in SE(3)

Selig, JM (2007). Curves of stationary acceleration in SE(3).*IMA Journal of Mathematical Control and Information.*24 (1), pp. 95 - 113.

##### A screw theory of Timoshenko beams

Selig, JM and Ding, X (2009). A screw theory of Timoshenko beams.*Journal of Applied Mechanics, Transactions ASME.*76 (3), pp. 1 - 7.

##### Rigid body dynamics using Clifford algebra

Selig, JM and Bayro-Corrochano, E (2010). Rigid body dynamics using Clifford algebra.*Advances in Applied Clifford Algebras.*20 (1), pp. 141 - 154.

##### On the geometry of the homogeneous representation for the group of proper rigid-body displacements

Selig, JM (2013). On the geometry of the homogeneous representation for the group of proper rigid-body displacements.*Romanian Journal of Technical Sciences - Applied Mechanics.*58 (1-2), pp. 5 - 28.

##### Rational interpolation of car motions

Selig, JM (2015). Rational interpolation of car motions.*Journal of Mechanisms and Robotics.*7 (3).

##### Quadratic constraints on rigid-body displacements

Selig, JM (2010). Quadratic constraints on rigid-body displacements.*Journal of Mechanisms and Robotics.*2 (4).

##### On the line geometry of rigid-body inertia

Selig, JM and Martins, D (2014). On the line geometry of rigid-body inertia.*Acta Mechanica.*225 (11), pp. 3073 - 3101.

##### A Class of Explicitly Solvable Vehicle Motion Problems

Selig, JM (2015). A Class of Explicitly Solvable Vehicle Motion Problems.*IEEE Transactions on Robotics.*31 (3), pp. 766 - 777 (11).

##### Persistent rigid-body motions and Study's "Ribaucour" problem

Selig, JM and Carricato, M (2016). Persistent rigid-body motions and Study's "Ribaucour" problem.*Journal of Geometry.*108 (1), pp. 149-169.

##### On the use of the Klein quadric for geometric incidence problems in two dimensions

Rudnev, M and Selig, JM (2016). On the use of the Klein quadric for geometric incidence problems in two dimensions.*Siam Journal on Discrete Mathematics.*30 (2), pp. 934 - 954 (21).