**On the Plane Symmetric Bricard Mechanism**

This talk will outline some recent work on the plane symmetric Bricard 6R mechanism. A simple method based on the dimensions of intersecting varieties in the Study quadric is used to show that the mechanism is mobile. The degree of the motion of the third link (the one adjacent to the plane of symmetry) relative to the plane of symmetry is found. The degree and genus of the motion of the third link relative to the first link is also found. This curve in the Study quadric is given as the intersection of the variety generated by the RR dyad formed by second and third joints with the variety of displacements that keep the fourth joint axis in the special linear line complex whose axis is the axis of the first joint. Finally, the motion of the symmetry plane when the second link is fixed is considered. The symmetry planes comprise the common tangent planes to a pair of circularly symmetric hyperboloids.

Jon Selig graduated from the University of York, with a B.Sc. in Physics in 1980. He went to study in the Department of Applied Mathematics and Theoretical Physics at the University of Liverpool and was awarded a Ph. D. in 1984 for work on the topology configuration spaces of identical particles. From 1984 to 1987 he was a postdoctoral research fellow in the design discipline of the Open University, studying robot gripping. He joined the Department of Electrical and Electronic Engineering at South Bank Polytechnic in 1987. His main research results include, a new classification of the Reuleaux lower pairs using Lie theory techniques, a modern statement and proof of the “Principle of Transference” using the representation theory of groups, a Lie algebraic approach to the dynamics of serial robots latter extended to parallel robots and walking machines, the introduction of a novel Clifford algebra for expressing and solving problems in three dimensional Euclidean geometry and a classification of Lie triple sub-systems of se(3). He retired in 2022 but remains active researching into applications of modern geometry to problems in robotics.