• Introduction to kinematics - Chapter 1
Overview of basic kinematic concepts: displacements, invariants of a displacement, vector-matrix representation, Plucker coordinates for lines. Collected in Notes Chapter 1 .
• Introduction to robot kinematics - Chapters 2 and 3
Overview of traditional forward and inverse kinematics for serial robots. Collected in Notes Chapter 2-3 .
• Grassmann algebra
Brief introduction to Grassmann algebra as a building block
for Clifford algebras.
Underlying vector space, outer product, multivectors.
• Clifford algebras, lecture 1
General definition of Clifford algebras and basic examples.
Underlying vector space, geometric product, dimension,
• Clifford algebra, lecture 2
The Clifford algebra of the projective space PR3 with a
Construction of Clifford algebras using different vector
spaces and metrics.
• Clifford algebra, lecture 3
Geometric entities and group elements within the Clifford algebra
of dual quaternions.
Lines, points, directions and planes. Rotations and translations
and the action on geometric entities.
• Robot forward kinematics
Forward kinematics of serial robots in the framework of
Clifford algebras. Lectures 1 and 2.
Absolute and relative forward kinematics. Composition
of local displacements and screw displacements.
Workspace and inverse kinematics.
• Introduction to kinematic synthesis
Definitions related to kinematic synthesis.
Task specification, type synthesis and dimensional synthesis.
• Introduction to kinematic synthesis 2
Mobility and techniques to state design equations.
• Introduction to kinematic synthesis 3
Overview of open problems in synthesis.
Design equations using robot forward kinematics.
• Introduction to kinematic synthesis 4
Kinematic synthesis example.
Spatial, serial 4R chain.
• Kinematic synthesis for tree topologies 1
First lecture of a series on synthesis for tree topologies.
Problem definition, graph representation.
• Lie algebras
Lecture on Lie groups and Lie algebras.
Subspaces and subalgebras, Lie bracket, the exponential map.
• Kinematic Synthesis for tree topologies 2
Second lecture of a series on synthesis for tree topologies.
Graph contraction, forward kinematics equations and mobility.
• Kinematic Synthesis for tree topologies 3
Third lecture of a series on synthesis for tree topologies.
Workspace and linkage locus space.
• Kinematic Synthesis for tree topologies 4
Fourth lecture of a series on synthesis for tree topologies.
Graph reduction, design equations, counting for exact synthesis.
• Kinematic Synthesis for tree topologies 5
Fifth lecture of a series on synthesis for tree topologies.
Graph matrices for dimensioning exact synthesis problem.
• Kinematic Synthesis for tree topologies 6
Sixth lecture of a series on synthesis for tree topologies.
Solvability, subgraphs and solvable subgraphs.
• Kinematic Synthesis for tree topologies 7
Final lecture of a series on synthesis for tree topologies.
Summary, open-source software.
Advanced Kinematic Synthesis
This course covers the basics for understanding the synthesis procedures for serial, parallel and tree articulated systems. Includes theoretical material on Clifford algebras, Grassmann algebra, etc., and material on robot forward kinematics, graph theory, task specification and kinematic synthesis.
Robotics Lab Seminar
The Robotics Lab seminar covers topics of interest in the robotic field. Includes background material, new developments and student presentations. Some of the slides can be found below.
• Introduction to graph theory for tree graphs
Basic graph theory definitions. Applications to the kinematic representation of mechanisms. Graphs for systems with multiple end effectors. Presentation.
• Introduction to kinematic synthesis
Basic concepts on kinematic synthesis theory. State of the art and applications. Presentation.
• ArtTreeKS: Kinematic solver for tree topologies
Program architecture, installation and running. Internal implementation of solvability and assembling of design equations. Presentation.