DYNAMIC MODELING OF ELASTIC ROBOT ARM IN BENDING AND TORSION

Öz

In this study, an elastic beam sliding through a prismatic joint having an arbitrarily given motion in a fixed coordinate system is investigated. It is assumed that elastic beam undergoing flexural in two planes and torsional elastic displacements, and elastic beam having a disk at one-end. Kinematics of prismatic joint is given as a 3Dspace motion in a fixed coordinate system. The prismatic joint is subjected to a propelling force from prismatic joint. With these assumptions, the differential equations of motion of the elastic beam are derived by using Hamilton’s Principle. Besides, the equations of motions of the system are derived as ordinary differential equations by using the Assumed Modes Method. These equations are solved and some sample mode shapes of the vibrations are presented as graphics. 

Anahtar Kelimeler

• Elastic beam,prismatic joint,flexural vibrations,torsional vibrations

EĞİLME VE BURULMAYA MARUZ ELASTİK ROBOT KOLUNUN DİNAMİK MODELİ

Öz

Bu çalışmada, uzaydaki sabit bir eksen takımına göre hareketi önceden belirlenmiş bir mafsal içinde hareket
eden elastik çubuk ele alınmıştır. Elastik çubuğun iki eksene göre eğilmeye ve kendi ekseni etrafında burulmaya maruz kaldığı ve çubuğun ucunda bir disk olduğu kabul edilmiştir. Kayar mafsalın sabit bir eksen takımına göre kinematiği üç boyutlu olarak verilmektedir. Elastik çubuğun kayar mafsal içindeki hareketini kayar mafsaldan uygulanan tahrik kuvveti temin etmektedir. Bu kabuller altında elastik çubuğun hareket denklemleri Hamilton Prensibi ile elde edilmiştir. Ayrıca, Kabul Edilmiş Modlar yöntemi kullanılarak sistemin hareket denklemleri adi diferansiyel denklem takımları şeklinde elde edilmiştir. Bu denklem takımları çözülerek elde edilen titreşim biçimleri grafikler şeklinde sunulmuştur.

Anahtar Kelimeler

• Elastik çubuk,prizmatik mafsal,eğilme titreşimleri,burulma titreşimleri

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