The camera post shouldn't be too long, since it will be difficult to handle, but on the other hand, the longer it is, the more resistance to rotation it provides. I decided that 400 mm should do. I also wanted the center of gravity to be at the upper 1/4 of the post's length, thus 100 mm from the post plate.
The post plate and cam plate should extend behind the camera, since the head of the square neck bolt would stick up a little. Our cam has a total length of 162 mm according to the manual. The tripod receptacle should then be somewhere in the center, so the cam plate should be about 80 mm between the camera screw and the bolt to secure the cam plate. Plus some margin for stability - 120 mm seems fine. The post plate should be a little longer, since we are able to trim the cam plate back and forth. 140 mm seems enough. Both plates are made of 50 x 5 mm aluminum bars. I don't think wider plates are needed, and 5 mm is because the collars of the sockets are also 5 mm thick.
Out of curiosity, how many counterweight washers would I need? To figure out
that in theory, we have to use some simple mechanics formulas to calculate
the torque of the entire rig, with cam mounted on. As I don't need any
high-precision result, I'm gonna simplify the design. I will exclude holes,
slots, screws and nuts and only calculate with "solid" objects.
To keep an object in balance, the sum of all forces has to be zero, as well
as the sum of all (positive and negative) torque. The black triangle
represents the wanted center of gravity and center of rotation. We have, in
this simplified setup, four forces: The cam (F1), the plates
(F2), the post itself (F3) and the counterweights
(F4). I assume the sockets are a part of the post itself, since
they don't weight much and they will not change the post's center of
gravitation. The formula for calculating torque is quite simple. The torque
is the gravity force (Newton) at a 90° angle to the center of rotation,
multiplied with the distance (meter) from the center of rotation:
t = F · d (Nm)
So, now we need to find the forces. According to the manual of the cam, it weights 705 g including battery. Multiplied with the constant for acceleration g (9.81), we get the force:
F1 = 0.705 · 9.81 » 6.92 N
The aluminum bars, which the plates are made of, are 0.66 kg per meter, according to the manufacturer's spec sheet. We use 120 + 140 mm which makes 0.26 meter:
Weight = 0.66 · 0.26 » 0.173 kg
F2 = 0.173 · 9.81 » 1.70 N
The post itself is made of an aluminum pipe which, according to the spec sheet, is 0.21 kg per meter. We use 0.4 meter, so:
Weight = 0.21 · 0.4 » 0.08 kg
F3 = 0.08 · 9.81 » 0.78 N
The 4th force (F4) is the one we are trying to figure out. So, let's calculate some torque! (I'm always assuming the center of gravity is in the center of the object itself).