Related Experiment Video
Updated: Sep 20, 2026

Kinematic Analysis Using 3D Motion Capture of Drinking Task in People With and Without Upper-extremity Impairments
Published on: March 28, 2018
A kinematic theory of rapid human movement. Part IV: a formal mathematical proof and new insights
Réjean Plamondon1, Chunhua Feng, Anna Woch
1Ecole Polytechnique de Montréal, Laboratoire Scribens, Département de génie électrique, P.O. Box 6079, Station Centre-ville, Montréal, Québec H3C 3A7, Canada. rejean.plamondon@polymtl.ca
Abstract:
A few years ago a kinematic theory was proposed to study and analyze rapid human movements. The theory relies on a model of a synergy made up of two neuromuscular systems, one agonist and the other antagonist to the movement. Representing these systems with lognormal impulse responses, it is predicted that the velocity profile of a fast movement will be described by a delta-lognormal equation. So far, many studies have been conducted to test and empirically validate the theory. This paper presents an extended mathematical proof of the model. The proof is based on the Central Limit Theorem under the assumption that a law of proportionate effect governs the cumulative time delays of a sequence of dependent subprocesses constituting a neuromuscular system. Furthermore, a detailed interpretation of the parameters of the delta-lognormal equation, in terms of movement time and amplitude, response time and time delays, is discussed, providing new insights into the properties of the model with respect to neuromuscular system activity and movement generation.
Related Concept Videos
Kinematic Equations - III
Using the kinematic equations,...
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: Problem Solving
Kinematic Equations - I
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...
Rotation with Constant Angular Acceleration - II
The first...

