Gear train system dynamics

1. Feb 17, 2014

xzibition8612

1. The problem statement, all variables and given/known data

See attachment.

2. Relevant equations

3. The attempt at a solution
Equations (1) and (2) describe this gear train system. I'm confused about them.

For (1):
If I rewrite it (∑F=0 format) I get:
T-T1-Jθ''-Bθ' = 0
The figure clearly shows θ1 positive spinning towards the bottom. Why then is T1 negative if it is spinning in the same direction as θ1? I understand the inertia and damping is always opposite to the defined positive direction.

For (2):
T2-TL-Jθ''-Bθ' = 0
Since the figure doesn't show the direction TL is going, why is it negative?

Also why is there a T1 and T2 if I only apply a load T? Shouldn't it just be T-Jθ''-Bθ' = 0 ? Where did T1 and T2 come from if I only applied T? And what exactly is a load torque?

Now I'm thinking isn't it physically impossible for a single shaft to have two torques going in opposite directions?

I'm obviously very confused on this. Any help would be appreciated.

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