Search results for " planar mechanisms"

showing 2 items of 2 documents

Tractional Motion Machines extend GPAC-generable functions

2012

In late 17th century there appeared the Tractional Motion instruments, mechanical devices which plot the curves solving differential equations by the management of the tangent. In early 20th century Vannevar Bush’s Differential Analyzer got the same aim: in this paper we’ll compare the Differential Analyzer mathematical model (the Shannon’s General Purpose Analog Computer, or GPAC) with the Tractional Motion Machine potentials. Even if we will not arrive in defining the class of the functions generated by Tractional Motion Machines, we’ll see how this class will strictly extend the GPAC-generable functions.

tractional motionlinkagesAnalog computationGPACnonholonomic constraintsAnalog computation; tractional motion; GPAC; computable functions; planar mechanisms; linkages; nonholonomic constraintscomputable functionsplanar mechanismsAnalog computation tractional motion GPAC computable functions planar mechanisms linkages nonholonomic constraints
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Tractional Motion Machines: Tangent-Managing Planar Mechanisms as Analog Computers and Educational Artifacts

2012

Concrete and virtual machines play a central role in the both Unconventional Computing (machines as computers) and in Math Education (influence of artifacts on reaching/producing abstract thought). Here we will examine some fallouts in these fields for the Tractional Motion Machines, planar mechanisms based on some devices used to plot the solutions of differential equations by the management of the tangent since the late 17th century.

Computer scienceDifferential equationAnalog computerdifferential equationsTangentMotion (geometry)educational artifactscomputer.software_genrePlot (graphics)planar mechanismslaw.inventiontractional motionPlanarVirtual machinelawComputer graphics (images)Analog computationAnalog computation; tractional motion; planar mechanisms; educational artifacts; differential equationsUnconventional computingcomputerAnalog computation tractional motion planar mechanisms educational artifacts differential equations
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