Page 113 - Robotics Designing the Mechanisms for Automated Machinery
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102 Dynamic Analysis of Drives
Hence,
From the initial conditions, for t = 0,0 = 0, and 0 = a> 0, it follows that
Thus,
Differentiating Equation (3.158) we obtain for ct)(t):
For torque proportional to speed,
After transformation, this equation can be rewritten as
or
where a> is a composite solution of two components: (0 = 0)^ + 0)^
The homogeneous solution CO Q may be found in an exponential form. Thus,
Substituting the exponential form into the homogeneous variant of Equation (3.160),
we find for b
The partial solution ^ is sought in the form
