How To Calculate True Position

Electrical engineers design and build electrical devices such as printed circuit boards and associated mechanical components. The first step in this process is producing a computer-aided design drawing that outlines the locations of wires, bonding pads and drilled holes. True position is the deviation of a feature on the product from its theoretical position on a drawing, and this position can be calculated using simple formulas.

The first step in determining the true position is to carry out measurements on the product and compare these measurements to the original drawings. This process makes use of standard engineering tools, including micrometers, height gauges and calipers.

Suppose a product consists of a single plate with a single drilled hole. In the following measurements, the plate origin (0,0) in standard Cartesian (x,y) coordinates is assumed to be on the bottom left-hand side of the plate. A caliper can be used to determine the position of the closest and farthest points of the hole on the x and y axes. For the sake of this example, assume that the closest and farthest measurements on the x axis are 15 mm and 20 mm, and the closest and farthest measurements on the y axis are 35 mm and 40 mm.

The centerline of a hole is calculated using the closest and farthest measurements of the hole on each of the coordinate axes. To calculate the centerlines on each axis use the following formula: center line = closest position + (farthest position – closest position)/2. Following the example in section 2, the center lines of the single hole on each axis are as follows: center line on x axis = 15 + (20 – 15 )/2 = 17.5 mm, and center line on y axis = 35 + (40 – 35)/2 = 37.5 mm.

True position is the deviation between the theoretical position on a drawing and the actual position, measured as the centerline, on the final product. True position can be calculated using the following formula: true position = 2 x (dx^2 + dy^2)^1/2. In this equation, dx is the deviation between the measured x coordinate and the theoretical x coordinate, and dy is the deviation between the measured y coordinate and the theoretical y coordinate. Following the example, if the theoretical coordinates of the drilled hole are (18 mm, 38 mm) then the true position is: true position = 2 x ((18 – 17.5)^2 + (38 – 37.5)^2)^1/2 = (0.25 + 0.25)^1/2 = 0.71 mm.