Related Experiment Video
Updated: May 13, 2026

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
Published on: September 24, 2017
3D kinematics using dual quaternions: theory and applications in neuroscience
Guillaume Leclercq1, Philippe Lefèvre, Gunnar Blohm
1Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université Catholique de Louvain Louvain-la-Neuve, Belgium ; Institute of Neuroscience, Université Catholique de Louvain Brussels, Belgium.
Abstract:
In behavioral neuroscience, many experiments are developed in 1 or 2 spatial dimensions, but when scientists tackle problems in 3-dimensions (3D), they often face problems or new challenges. Results obtained for lower dimensions are not always extendable in 3D. In motor planning of eye, gaze or arm movements, or sensorimotor transformation problems, the 3D kinematics of external (stimuli) or internal (body parts) must often be considered: how to describe the 3D position and orientation of these objects and link them together? We describe how dual quaternions provide a convenient way to describe the 3D kinematics for position only (point transformation) or for combined position and orientation (through line transformation), easily modeling rotations, translations or screw motions or combinations of these. We also derive expressions for the velocities of points and lines as well as the transformation velocities. Then, we apply these tools to a motor planning task for manual tracking and to the modeling of forward and inverse kinematics of a seven-dof three-link arm to show the interest of dual quaternions as a tool to build models for these kinds of applications.
Related Concept Videos
Kinematic Equations for Rotation
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
Kinematic Equations - II
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
Kinematic Equations - III
Using the kinematic equations,...
Kinematic Equations - I
Kinematic Equations: Problem Solving
Three-Dimensional Force System
