Design and analysis of an optoelectronic inclinometer for simultaneous measurement of inclinations along two orthogonal directions

Abstract

Conventional inclination measurement systems such as precision vials and capacitance measuring systems can measure inclination in only one direction at a time. We present what is believed to be a new optoelectronic system that can measure inclination angles along two orthogonal directions simultaneously by using a simple pendulum, two mirrors, a 2D position-sensing detector (PSD), and a laser diode. The light ray from the laser is projected onto a mirror that is fixed to a pendulum whose relative angle modifies in response to inclination changes of the inclinometer's housing. The light ray reflected by the mirror is sensed by the PSD, after which the signal can be interpreted by a PSD signal processor, recorded, or output to a computer. This study uses skew-ray tracing methodology to obtain implicit nonlinear system equations to model the relations of the relative inclination angles of the various components, PSD position, and world frame. A first-order Taylor series expansion is used to obtain a linear form of the system equations. To validate the proposed methodology, an actual prototype system is built and experimental results show that the performance of this system is excellent.