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. / Master of Science

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The valveless micropump holds great potential for the biomedical community in applications such as drug delivery systems, blood glucose monitoring and many others. It is also a critical component in many a lab-on-a-chip device, which in turn promises to improve our treatment and diagnosis capabilities for diseases such as diabetes, tuberculosis, and HIV/AIDS. The valveless micropump has attracted attention from researchers on the grounds of its simple design, easy manufacturability and sensitive fluid handling characteristics, which are all important in biomedical applications. The pump consists of a pump chamber with a diffuser and nozzle on opposing sides of the pump chamber. The flow into the diffuser and nozzle is induced by an oscillating piezoelectric disc located on top of the pump chamber. The nozzle and diffuser rectify the flow in one direction, due to different pressure loss coefficients. The design process however is complex. In this study, we investigate the characteristics of a diffuser / nozzle based micropump using detailed computational fluid dynamic (CFD) analyses. Significant parameters are derived using the Buckingham-Pi theorem. In part based on this, the respective shapes of the diffuser and of the nozzle of the micropump are selected for numerical investigation. Hence the influence of the selected parameters on the flow rate of the micropump is studied using three-dimensional transient CFD analyses. Velocity profiles from the CFD simulations are also compared to the Jeffery-Hamel solution for flow in a wedge shaped channel. Significant similarities exist between the data and the predicted Jeffery-Hamel velocity profiles near the exit of the diffuser. Three different diffuser geometries were simulated at three frequencies. The flow rate and direction of flow are shown to be highly sensitive to inlet and outlet diffuser shapes, with the absolute flow rate varying by as much as 200% for the geometrical perturbations studied. Entrance losses at both the diffuser inlet and nozzle inlet appear to dominate the flow resistance at extremely laminar flow conditions with the average Reynolds number of Reave ≈ 500. / AFRIKAANSE OPSOMMING: Die kleplosemikropomp hou groot potensiaal in vir die biomediese gemeenskap in toepassings soos medisyne dosering sisteme, bloed glukose monitering en baie ander. Dit is ook ’n kritiese komponent in “lab-on-chip” sisteme, wat beloof om die behandeling en diagnose van siektes soos suikersiekte, tuberkulose enMIV/VIGS te verbeter. Die kleplose mikropomp het tot dusver die aandag van navorsers geniet as gevolg van sy eenvoudige ontwerp, maklike vervaardiging en sensitiewe vloeistof hantering. Hierdie kenmerke is krities inmenige biomediese toepassings. Die pomp bestaan uit ’n pompkamer met ’n diffusor en ’n mondstuk aan teenoorstaande kante van die pompkamer. Vloei in die diffusor en mondstuk in word geinduseer deur ’n ossillerende piëso-elektiese skyf wat bo-op die pompkamer geleë is. Weens verskillende druk verlies koëffisinëte van die diffusor en diemondstuk word die vloei in een rigting gerig. Die ontwerp-proses is egter kompleks. In hierdie studie word die eienskappe van die diffusor /mondstuk ondersoek deur gebruik temaak van gedetailleerde numeriese vloei-dinamiese analises. Belangrike parameters word afgelei deur gebruik te maak van die Buckingham-Pi teorema. Gedeeltelik gebaseer hierop word die onderskeidelike vorms van die diffusor en die mondstuk van die mikropomp geselekteer vir numeriese ondersoek. Gevlolglik word die invloed van die geselekteerde parameters op die vloei tempo van diemikropomp ondersoek deur gebruik temaak van drie-dimensionele tyd afhanklike numeriese vloei-dinamiese analises. Snelheids profiele van hierdie simulasiesword vergelykmet die Jeffrey-Hamel oplossing vir die vloei in ’n wigvormige kanaal. Daar is oorwegende ooreenkomstighede tussen hierdie data en die voorspelde Jeffrey-Hamel snelheids profiele veral by die uitgang van die diffusor. Drie verskillende diffusor vorms is by drie frekwensies gesimuleer. Daar is bewys dat die vloei tempo en vloeirigting baie sensitief is vir inlaat- en uitlaat diffusor vorms en dat die absolute vloei tempo kan varieermet soveel as 200%vir die geometriese versteuringswat ondersoek is. Inlaat verliese by beide die diffusor inlaat en die mondstuk inlaat, blyk om die vloei weerstand te domineer waar die vloei uiters laminêr ismet ’n gemiddelde Reynolds getal van Regem ≈ 500