This past weekend, I managed to finish assembly on one of the linear motion axes that will go into my desk and carry out a motion repeatability test. Based on the error budget, I know that the most significant source of random error motion in my sensitive direction (height) is rotation of the slider within the box way due to radial clearance. Here I am using the familiar “laser pointer method” to determine the actual angular error in my axis by measuring the resulting sine error as projected on a surface a known distance away.
This time, I am projecting onto a wall 2770 mm away from the most proximal position of my slider (measuring from the most proximal position is conservative since it overestimates the angular error at more distal positions along the axis). I ran my slider from end to end three times and recorded the location of the projected beam at each end position. The most extreme vector displacement between projected points I observed was 20 mm, corresponding to end-to-end motion along the axis. Points projected from the same position along the axis were consistently within 3 mm of each other. Part of these deviations could be attributed to the cosine error coming from not squaring the axis perfectly to the wall, but the bulk of it comes from sine error due to slider rotation.
These results indicate an angular error of 0.4° from one end of the axis to the other, and less than 0.065° at any one point along the range of motion. Theoretically, most of the end-to-end error will be systematic and mappable since it is due to straightness and parallelism errors in the boxway, while the errors observed when the slider is at the same position are due to clearance and therefore random or non-mappable. In this instance, however, I do not plan to map the errors in my desk, so I will continue to lump the systematic and random errors together in my error budget spreadsheet. I also updated the random translational error for the attachment point of my slider to my boxways to match the observed end-to-end angular error. The new random translational error is 0.22 mm (assumed to be the same in all three directions). This is significantly greater than the 0.1 mm I initially specified, but still keeps my overall height error within the apportioned 5-mm range.