dc.contributor.author	Gilbert, Gregory S. Jr.	en
dc.contributor.committeechair	Saunders, William R.	en
dc.contributor.committeemember	Baumann, William T.	en
dc.contributor.committeemember	Robertshaw, Harry H.	en
dc.contributor.department	Mechanical Engineering	en
dc.date.accessioned	2014-03-14T20:51:13Z	en
dc.date.adate	1998-04-01	en
dc.date.available	2014-03-14T20:51:13Z	en
dc.date.issued	1998-03-17	en
dc.date.rdate	1999-04-01	en
dc.date.sdate	1998-03-17	en
dc.description.abstract	This thesis presents scaling methods for sizing a prototype micro prismatic revolute (PR) manipulator actuated by permanent magnet (PM) direct current (d.c.) gearmotors. Dimensional analysis was the principle tool used in this investigation, and addressed the problems of scaling a trajectory planner, control law, and gearmotors that exhibit internal nonlinear friction. Similitude methods were used to develop a scaleable two degree-of-freedom trajectory planner from a third order polynomial. Scaling laws were developed from Buckingham's Pi theorem to facilitate the selection process of gearmotors. Nondimensional, nonlinear, differential equations were developed to describe viscous, Coulomb and static friction in comparative PM d.c. motors. From the insights gained through dimensional analysis, a scaleable controller based on the computed torque method was developed and implemented with a cubic trajectory planner. Model and prototype PR manipulator systems were simulated using a hybrid Matlab/Simulink simulation scheme. Experimental systems were constructed with dissimilar model and prototype motors. Control was provided by an AT class PC equipped with 12-bit A/D, D/A cards operating at a sample rate of 100 Hz. The control algorithm was written in Borland 3.1 C for DOS. Results from the experimental testing showed excellent agreement between the test and simulated data and verified the viability of the scaling laws. The techniques presented in this thesis are expected to be applicable to any application that involves scaling PM d.c. micro gearmotors that have significant internal friction terms. These simple, practical tools should be especially beneficial to designers of micro robotic systems.	en
dc.description.degree	Master of Science	en
dc.identifier.other	etd-3198-143639	en
dc.identifier.sourceurl	http://scholar.lib.vt.edu/theses/available/etd-3198-143639/	en
dc.identifier.uri	http://hdl.handle.net/10919/36599	en
dc.publisher	Virginia Tech	en
dc.relation.haspart	intro.pdf	en
dc.relation.haspart	chap1.pdf	en
dc.relation.haspart	chap2.pdf	en
dc.relation.haspart	chap3.pdf	en
dc.relation.haspart	chap4.pdf	en
dc.relation.haspart	chap5.pdf	en
dc.relation.haspart	chap6.pdf	en
dc.relation.haspart	appendix.pdf	en
dc.relation.haspart	notes.pdf	en
dc.rights	In Copyright	en
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/	en
dc.subject	Dimensional Analysis	en
dc.subject	Buckingham Pi Theorem	en
dc.subject	Similitude	en
dc.subject	Scaling	en
dc.subject	Brushed DC Permanent Magnet Motors	en
dc.subject	Coulomb	en
dc.subject	Viscous	en
dc.subject	Static	en
dc.subject	Nonlinear Friction	en
dc.subject	Computed Torque Control	en
dc.title	Scaling a Prismatic Revolute Joint (Pr) Manipulator Using Similitude and Buckingham Pi Techniques	en
dc.type	Thesis	en
thesis.degree.discipline	Mechanical Engineering	en
thesis.degree.grantor	Virginia Polytechnic Institute and State University	en
thesis.degree.level	masters	en
thesis.degree.name	Master of Science	en

Scaling a Prismatic Revolute Joint (Pr) Manipulator Using Similitude and Buckingham Pi Techniques

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