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Kinematisk och dynamisk modellering av den haptiska enheten TAU i sex frihetsgrader
KTH, School of Industrial Engineering and Management (ITM), Machine Design (Dept.).
2009 (Swedish)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Kinematic and Dynamic Modeling of 6-DoF TAU Haptic Device (Swedish)
Abstract [en]

The thesis presents an optimally designed kinematic structure for a new 6-DOF haptic device

based on TAU configuration. The configuration of the TAU-2 proposed by Suleman Khan and

Kjell Andersson [1] was modified and its mobility was verified by using Grübler criterion to

have a 6 DOF. Analytical kinematic models for the inverse and forward kinematics were

developed for the haptic TAU configuration to determine a set of optimal design parameters.

Kinematic performance indices such as volume of the workspace, kinematic isotropy and pay

load index, were defined based on the singular values of the Jacobian matrix. The Jacobian

matrix was scaled to homogenize the physical units. The Jacobian matrix dependent on the

position and orientation of the end-effector gives local isotropy and pay load index, so global

design indices were defined, which represent the performance of the mechanism in the whole

workspace. A multi-objective function was defined based on the minimum of the global design

indices in order to find a set of optimal design parameters. Genetic algorithm (GA) was used for

optimization due to the nonlinearity of the multi-objective function. The optimal design

parameters were obtained by minimizing the payload index while maximizing the volume index

and isotropy indices.

A close form dynamic model was developed using Lagrange mechanics to describe the dynamic

behavior of the configuration. A trigonometric helical trajectory was developed in Cartesian

space for each degree of freedom for the moving platform while moving along the trajectory

Abstract [sv]

Detta arbete presenterar en optimalt utformad kinematisk struktur för en ny 6 frihetsgraders

haptisk enhet baserad på en TAU-konfiguration. Den konfigurationen för TAU-2 som var

föreslagen av Suleman Khan och Kjell Andersson [1] modifierades och den nya

konfigurationens rörlighet i 6 frihetsgrader verifierades med hjälp av Grüblers kriteria. Modeller

för direkt och invers kinematik har utvecklats för att användas vid den kinematiska optimeringen

av strukturen.

För optimering av strukturen definierades ett antal designparametrar tillsammans med tre index.

De index som definierades var; arbetsområdets volym, kinematisk isotropi samt nyttolast. Både

den kinematiska isotropin och nyttolast definierades utifrån singulära värden hos Jacobimatrisen.

Jacobimatrisen har även skalats för att få en likformighet i fysikaliska enheter hos dess element.

En ”multi-objective” funktion har definierats baserat på dessa tre index för att få en optimal

konfiguration som ger en kombination av designparametrar som maximerar isotropi, volym och

minimerar nyttolast.

Förutom de kinematiska modellerna har även en invers dynamisk modell utvecklats baserat på

Lagrange formalism. För att utvärdera den inversdynamiska modellen har även en bana i rymden

definierats längs vilken alla frihetsgrader hos enhetens plattform aktiveras.

Place, publisher, year, edition, pages
, MMK 2009:93 MKN 021
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-100140OAI: diva2:542850
Available from: 2012-08-03 Created: 2012-08-03 Last updated: 2012-08-03Bibliographically approved

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