CNC Math (Cont.)

Here is the math for using pulleys on a vertical plane. Using the formula Force = mass * gravity and Work = Force * distance. I substituted Force into the work equation. Input the knowns, distance = 1.2 m, max work capable per the specs of the motor = 4.6 Nm, and gravity = 9.8 m/s^2. Re-wrote the equation to solve for mass (kg).

I then calculated for adding additional wheels to multiple the force of the motor.  Each multiplier equals each line connected to the mass which in the illustration has 6 total top and bottom.

That still was not enough force multiplier.  I then calculated gearing and settled on 1:3 which means that for each rotation of the motor, the mass will move a little over 5/16 of an inch.

CNC the math

Here is the math, as I see it, for calculating the max mass that a NEMA 32 ( http://www.buildyourcnc.com/electronicscombo.aspxcan ) can lift in a vertical plane using a 1/2 inch diameter threaded rod ( http://www.buildyourcnc.com/CNCMachineMechanicalParts.aspx ).  First, I calculated the circumference of the rod and labeled that x. Then used the known distance up for one turn as y.  Calculated the degrees tangent O using opposite over adjacent. 

 

Using the formula Force = mass * gravity * cosO and Work = Force * distance.  I substituted Force into the work equation. Input the knowns, degrees = 17.7, distance = 1.2 m, max work capable per the specs of the motor = 4.6 Nm, and gravity = 9.8 m/s^2.  Re-wrote the equation to solve for mass (kg).

 

The result is a gearing for a 1:1 ratio.  I then calculated the result for other gearing ratios to find a larger mass.  Unfortunately, the best gearing for a 14 lbs is set at 1:6 which means that for each rotation of the stepper motor, the threaded rod will move an object up a little over a 1/16 of an inch.

CNC Build (Cont.)

Pic of it leaning during construction.

CNC Build (cont.)

Look its a bed rail!!  Base frame assembled for CNC Leaner but not confirmed it is square yet.  When the X-axis gantry is assembled, I will lock the frame down.  Unfortunately, measured/planned incorrectly and lost inches from the Y-axis (should have cut the L-shapes longer).  It probably will not be a full 48 inches of cutting surface once the Z-axis is constructed.

CNC Build (Cont.)

CNC build (cont.)

Beginning CNC build