Simple 6 DOF Translation and Rotation Stages

I had the requirement to control a device in 6 degrees of freedom (DOF). There were 3 motorized translation stages to control the position of the tool in 3D space and 3 rotary motorized stages to control its orientation. Although it could be thought as a robot arm having 3 prismatic joints and 3 revolute joints, I did not want to involve complex forward and inverse kinematics for this simple testing equipment.

Here is an example transformation. By arranging rotational axes of rotary motorized stages to intersect at the tool, a simple direct 6 DOF control could be achieved. The following figures show schematic diagram and 3D drawing for the equipment that I designed.

Capacitor selection for a Crystal Oscillator

A typical crystal oscillator circuit and an example layout design are shown in the figures. A crystal manufacturer normally specifies the load capacitance, C_L, needed for a crystal in its datasheet. This value is the load seen by the crystal which is in series with C₁ and C₂, including all parasites. Typically, overall stray capacitance, C_stray, for pin, board, and PCB trace is between 2 pF and 7 pF. The relation between them can be represented by the following formula.


C_L=(C₁ * C₂)/(C₁ + C₂) + C_stray

C₁ and C₂ are normally chosen to have equal value. Therefore,

C₁ = C₂=2 * (C_L - C_stray)

For example, assume that C_stray is 4 pF and crystal load capacitance C_L is 18 pF, C₁ = C₂= 28 pF. The normalized value of 30 pF can be used.