Vol. 8, No 1, 2010 pp. 45 - 56
DOI 10.2298/FUPCT1001045F
UDC 532.513"311" : 532.513"312"
DIFFERENCES BETWEEN SOURCE AND NEW FORM OF THE EULER-BERNOULLI EQUATION AND ITS SOLUTION
Mirjana Filipović
Mihajlo Pupin Institute, Volgina 15, 11000 Belgrade, Serbia
Abstract. In construction of complex robotic and related mechanisms, lightweight materials are often used and they are characterized by flexibility segments. To achieve precise and rapid control of motion of such a mechanism, it is necessary to synthesize their high fidelity model. This would be of great importance for its analysis and synthesis. The work in this paper starts from the first research in this area, and it includes the original form of the Euler-Bernoulli equation and its solution, which, compared with current knowledge, imposes the need for the expansion of the same equation from multiple points of view. The new form of the Euler-Bernoulli equation and its solution are based on current knowledge in robotics, as well as the knowledge of classical mechanics. This is the only way of how to fully preserve the information of the complexity of the kinematics and dynamics of elastic mechanisms.
Key words: Euler-Bernoulli equation, elasticity of link, coupling, kinematics, dynamics
RAZLIKE IZMEĐU IZVORNE I NOVE FORME EULER-BERNOULLI JEDNAČINE KAO I NJENOG REŠENJA
Pri konstrukciji složenih robotskih i sličnih mehanizama, često se koriste laki materijali koje karakteriše elastičnost segmenata. Radi postizanja precizne i brze kontrole kretanja takvih mehanizama potrebno je da se sintetizuje njihov visoko verodostojni model. To bi bilo od velike važnosti za njegovu analizu i sintezu. Polazi se od prvih istraživanja u ovoj oblasti, a to su originalna forma Euler-Bernoulli jednačine kao i njeno rešenje, što pri poređenju sa savremenim znanjima nameće potrebu proširenja istih jednačina sa više stanovišta. Nova forma Euler-Bernoulli jednačine, a takođe i njeno rešenje, se bazira na savremenim znanjima iz robotike, odnosno na znanjima klasične mehanike. To je jedini način da se kompletno sačuva informacija o složenosti kinematike i dinamike kretanja elastičnog mehanizma.
Ključne reči: Euler-Bernoulli jednačina, elastičnost linka, sprezanje, kinematka, dinamika
