Other Factors to Consider
Practical Center of Gravity as it Affects Gear Driven Positioners
- CG of a weldment is exactly in the center of asymmetrical weldment.
- "A" is a symmetrical weldment:There is no top or bottom, just
sides, the CG of a weldment is usually near the center of the weldment.
- The ends are two sides of 1" steel plate. Each end is 1x12x12 and weighs 40.8#. Each side is 1x12x34, weighs 115.6# x 2, plus 40.8# x2 equals 312.8#. (Steel weighs approximately .283 pounds/cubic inch.) If one end is secured to the table of a Gear Driven Positioner, the CG will be 18" out from or above the table. If either side, or the open top or bottom is secured to the table, the CG will be 6" above it.
- "B" is also a symmetrical weldment: A 2" plate rib has been
added in the middle, making the weldment a stiff column. the 2x10x34
steel rib weighs 192.7# so the weldment now weighs 505.5#. The rib being
right in the middle added weight equally in opposite directions from
center, so the CG is still in the dead center.
- "C" is an asymmetrical weldment: We want a box instead of a column, so we add a 2" thick bottom to weldment "A". 2x12x36 steel weighs 244.6# so total weight is not 557.6#. But the CG will not be at 7", halfway from top or bottom, because we added nothing to the top to balance the weight of the bottom. We made no change at either end, and the bottom is as much left as right, so the CG remains 18" in from either end.
- The CG always moves toward any part that is added to a
symmetrical weldment. Locating the CG is a function of movements.
"Moment" means force or tendency to product motion. A Moment is weight
multiplied by length (Arm). Like a lever. And like a lever, we must have
a hinge point, a reference plane. The top surface of a Gear Driven
Positioner's table is our reference plane. Load Capacity Tables give
ratings for various distances the CG is above the table, so this is very
handy. Whenever possible, weldments should be mounted with the heavy
side next to the table, so let's figure it that way.
- Each separate symmetrical part will have a known weight and
CG, and the CG will be a known distance from the table top surface.
Multiplying weight by distance (arm) gives the pound-inch (lbs-in)
moment of t5he part. Adding all the moments and dividing by total weight
gives the location of the CG of the weldment.
We don't need to take each end and each side separately because the side and ends make symmetrical mass weighing 312.8#, with the CG in the center of that mass. With the 2" plate between it and the table, the CG will be 8" above the table. 312.8# x 8" =2502.4 lb-in.
The 244.8# bottom's CG is 1" above the table.
244.8# x 1" = 244 lb-in.
Adding 244.8 lb-in and 2505.4 lb-in equals 2747.2 lb-in Total Moment. Dividing 2747.2 lb-in Total Moment by 557.6 Total Weight locates the CG 4.9" above table top surface.