Dual speed focuser
The Dual speed focuser is focusing mechanism in precision optics such as advanced amateur astronomical telescopes or laboratory microscopes.
Dual speed focuser can provide two focusing speed on a set of co-axial knobs.One for fast focusing and another for fine focusing when the film or CCD is near the perfect focus plane. This is different from two separate focusing knobs seen on low level microscopes. Another common reason to employ dual-speed focuser is the use of low focal length eyepieces, where the focus depth is short, requiring accurate focusing.
Dual speed focusing mechanism is often conbimed with Crayford focuser forming a Dual speed Crayford focuser in order to eliminate backlash effect during fine focusing.
The concept
Dual speed focuser design borrows the planetary gearing idea used in automobile gearboxs. However, in order to eliminate backslash, balls and axles are used instead of gears. All the transmission inside dual speed focuser is achieved via static friction.
The cylinder case of dual speed focuser is fixed on the telescope tube. 3 metal balls are placed and separated 120° between each other inside the case by a holder shelf. An input axle penetrates through the hole on the center of holder shelf and is pushed and tightened by 3 surrounding balls. The fine focusing knob connects to the input axle while the fast focusing knob connects to the holder shelf. On the other side, the axle from Crayford focuser is connected to the holder shelf.
When you rotate the fine focusing knob, the 3 balls are driven by input axle and rotate along the inner circumference of the case at slower speed. The metal balls then push the holder shelf and drive the output axle. As a result, rotating either of the focusing knobs will cause the other to rotate in the same direction.
Calculation
The angular velocity of input and output axle can be described as formula below:
Where the R and r are the radius of metal ball and input axle, the 
and 
are the angular velocities of input and output axle.
A 1:10 dual speed focuser has a gear ratio of 10 and R=4.5r. Thus the angular velocity ratio is actually 11. The gear ratio and velocity ratio should not be confused with each other.