The constrained motion
condition can be expressed, according to Alt, through the equation:
In real microscopic quantum systems, constrained motion
is a result of a strong confining force (electrostatic, rigid chemical bonds, etc.).
Arikan and Forsyth synthesized constrained motion
sequences by searching appropriate paths in this graph using a randomized search method  which starts with a set of paths in the graph randomly, scores each path and all possible mutations, does every possible mutation, compares the satisfaction of the constraints to the original path, accepts the mutations that are better than the original paths, repeats until no better path can be generated through mutations, and obtains the final path.
Chapter one, "Mechanical Design and Fabrication," includes sections on tools and shop processes, materials, physical principles of mechanical design, and constrained motion
. Chapter two covers "Working With Glass." Chapters are devoted to various classes of apparatus: vacuum technology, optical systems, detectors, thermal measurement devices, and so on.
The literature reports two broad approaches for the control of robots executing constrained motion: hybrid (force/position) control and impedance control.
In this formulation the control strategy does not optimize the transition between unconstrained and constrained motions but once the contact is established the method allows also to control the interaction force.
(21) This group compared immobilization and immediate constrained motion
using a tethering splint.
The almost 90 contributions cover a broad range of topics, including wing morphing, aircraft control, nonlinear aircraft ground dynamics, alcohol and air rage, and the geometry of constrained motion
. Papers begin with a summary introduction and conclude with a list of references.
Key words: Haptic Interface, shape, texture, roughness, exploration, control, constrained motion
, free motion
Udwadia and Kalaba have pictured the difference between the predicted free motion at each instant and the actual constrained motion
at the same time, uncovering a central principle of mechanics.
Work we have done for other disciplines includes an animation of the process of cell division in biology; an animation of the functional connectivity of devices in the master control room of a TV studio; an animation for the mathematics department, showing the evolution of complex geometrical forms from the constrained motions
of points, lines and circles; and an animation of a human heart (done for the cardiac unit at a local hospital).