Error of Archimedes spiral when applied in linearity compensation

Abstract

The polar coordinates equation of Archimedes spiral is ρ = ρ 0 + aθ , also known as uniform speed spiral. In a polar coordinate system, the polar radius ρ has linear relation with polar angle θ . This character could be used for linearity compensation in mechanical engineering, or metrical instrument. For example, it could be used for moment linearity compensation, the common configuration has a pivot axis on the pole, and a thin line wrap around the spiral on the turntable. The gravitation of a suspension used as constant pull, and the level polar radius as force arm, then it generates a liner moment when the Archimedes spiral rotating at uniform speed. But as the polar angle of tangent point on the plumb line changes at any moment, the polar radius on level direction isn’t linear with polar angle anymore, and the small error influences the effect of linearity compensation configuration. This paper presented the application of Archimedes spiral in linearity compensation, analyzed the theory error, and deduced the error equation by Mathematic theory. Using computer emulator, educed the precise errors of some dispersed points in common use, and provided according error tabulation. In engineering applications, engineers could consult this error tabulation and correct the points on Archimedes spiral, to realize accurately linearity compensation.