Page 93 - Robotics Designing the Mechanisms for Automated Machinery

82 Dynamic Analysis of Drives

Substituting Equation (3.55) into Equation (3.54) we obtain

or

For a> 2 we seek a solution in the form

Substituting Equation (3.58) into Equation (3.52) we obtain

or

From Equation (3.53) we derive

For the initial conditions at time t= 0 and speed CD = 0, we can rewrite Equation (3.61)
and extract the unknown constant A in the following way:

or

And finally we obtain the solution:

To calculate the time needed to achieve some speed of rotation co^ we derive the fol-
lowing equation from Equation (3.64):

From Expression (3.65) some particular cases can be obtained. For a constant resis-
tance torque a 2 = 0 we obtain