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D`ALAMBER`S PRINCIPLE OF SOLVING ROBOT DYNAMICS BY USING MATRICES OF ROTATIONAL TRANSFORMATIONS


MIKIÆ DANILO 1, GOLUBOVIÆ DRAGAN 2
1. UNIVERSITY OF KRAGUJEVAC, TECHNICAL FACULTY IN ÈAÈAK, SVETOG SAVE 65, 32000 ÈAÈAK , SERBIA AND MONTENEGRO, E-MAIL: MIKICDANILO@PTT.YU; 2. UNIVERSITY OF KRAGUJEVAC, TECHNICAL FACULTY IN ÈAÈAK, SVETOG SAVE 65, 32000 ÈAÈAK, SERBIA AND MONTENEGRO, E-MAIL:

Issue:

MOCM, Number 13, Volume III

Section:

Issue No. 13 - Volume III (2007)

Abstract:

The work gives the results of the research into the D’Alamber principle of solving the robot dynamics by using the matrices of rotational transformations, i.e. the work deals with the problem of robot mechanics, and the possibilities of the application of the basic equations of matrices of rotational transformations, in solving dynamics of a robot whose basic structure is based on joints that allow only rotation. The work also lists the Dynamic Models of the manipulator that can be made based on th use of the known laws of the Newton of Lagrange mechanics. As a result of the application of these laws, there are the equations that link the effects of the forces and their moments to the segments with kinematic parameters of the movement of the chain. Also, it gives the characteristics of the movement equations of the manipulator through the Lagrange- Oiler Method, as well as the Newton- Oiler equations, and D’Alamber equations. Since the mechanical structure of a robot represents a single joint-based mechanism, a robot is seen as a disassembled chain, and then a definition is made of a geometric approach to solving D`Alamber. There is a separate account of the cases that occur in practical realisations, so that a computer program can be made for checking the validity of the solutions to the D`Alamber principle in the tasks relating to the kinematics of the robot-manipulator. The work represents a part to a project which is being realised at the Technical Faculty in Èaèak, with an aim to develop mechanotronic systems, and its results are useful in solutions related to anthropomorphic robots, as well as in other applications in various areas of technology.

Keywords:

Kinematics pairs, speed, acceleration, kinetics energy, potential energy, driving force, gravity, centre of gravity, centrifugal force, the Coriolis force, translatory movement, rotational movement.

Code [ID]:

MOCM200713V03S01A0010 [0001794]


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