Abstract
This paper presents a generalized analytical method for the determination of velocities and accelerations in mechanisms having motion in either two or three dimensions. In this method of analysis, one first obtains independent-position equations for a particular point or for a particular link. The first derivative with respect to time of these position equations yields equations for obtaining the velocity of the point or the angular velocity of the link of interest; and the second derivative with respect to time furnishes new equations from which the desired accelerations may be found. Position vectors are expressed as complex numbers in exponential form because of the ease with which they may be differentiated, and also because numerical results are readily obtainable from the real and imaginary parts of the complex numbers.
