An autocollimator designed for measuring the three angular coordinates of a rotating object was examined. The impact of the principal primary errors of an autocollimation angular-measurement system on the error in measuring the axis position and magnitude of a rotating object was analyzed. A computer model of an autocollimation system was built based on describing object rotations using quaternions method. The autocollimation measurements algorithms were compared based on the quaternion and matrix models using the autocollimator parameters deviations effect on the total measurement error. Results of experimental research of the two versions of tri-coordinate autocollimation systems were described: one of them used a matrix model and another one – a quaternionic theoretical model. Autocollimator reflectors in the form of two-sided, tetrahedral and pyramidal prisms were investigated and rotation measurement errors were calculated.
Autocollimators are widely used for angular measurements in instrument-making and the manufacture of
elements of optical systems (wedges, prisms, plane-parallel plates) to check their shape parameters (rectilinearity,
parallelism and planarity) and retrieve their optical parameters (curvature radii, measure and test their flange focusing).
Autocollimator efficiency is due to the high sensitivity of the autocollimation method to minor rotations of the reflecting
control element or the controlled surface itself. We consider using quaternions to optimize reflector parameters during
autocollimation measurements as compared to the matrix technique. Mathematical model studies have demonstrated that
the orthogonal positioning of the two basic unchanged directions of the tetrahedral reflector of the autocollimator is
optimal by the criterion of reducing measurement errors where the axis of actual rotation is in a bisecting position
towards them. Computer results are presented of running quaternion models that yielded conditions for diminishing
measurement errors provided apriori information is available on the position of rotation axis.
A practical technique is considered for synthesizing the parameters of the tetrahedral reflector that employs the
newly-retrieved relationships. Following the relationships found between the angles of the tetrahedral reflector and the
angles of the parameters of its initial orientation, an applied technique was developed to synthesize the control element
for autocollimation measurements in case apriori information is available on the axis of actual rotation during monitoring
measurements of shaft or pipeline deformation.
We consider the design of a reflector to measure the rotation angles with respect to three axes by the autocollimation method. A quadrangular pyramidal reflector is proposed. An exact algorithm of angular measurements for yaw and pitch angles is considered. Two reflector variants are studied. In the first variant, the angles between the reflecting faces is 90°, in the second variant, these angles do not equal 90°. Algorithms are designed to determine the yaw, pitch and roll angles with two reflector variants. Reflector effectiveness is compared for autocollimation measurements of three rotation angles of an object.
The article is based on some researching considering the three-axis angle measuring autocollimation sensor. Such a sensor allows measuring the deformation of large constructed objects while receiving the information about all three angular freedom degrees. The feasibility of a special tetrahedral prism reflector, with two modes of operation is described and proved. The ability to synthesize such a reflector is proved mathematically; including the description of it’s both modes functioning. All algorithms were taken from the mathematical model of such a reflector functioning, which was created while the researching. First mode allows measuring the roll angle with high accuracy, and the second mode allows measuring the collimation angles, using different types of light reflected beams. So there are two ways to measure collimation angles: rough and precise. The algorithm for rough way of collimation angles measuring is quite similar to the roll algorithm measuring and used for the adjustment and for the initial setting the autocollimation sensor. The precise algorithm is used for the prime measuring in a complex with roll angle measuring to get full information of three-dimensional deformation of the object. The experimental stand was researched to confirm the correctness of all algorithms of the reflector and the sensor functionality in the whole. The technical characteristics of the experimental setup are presented.
The improved autocollimation system for measuring three-dimension angular deformations of pipe sections at large constructions as support tube of radio telescope mirror is analyzed. New type of the reflector for autocollimators is researched. The reflector is the trihedral mirror composition of three reflecting sides. It advantage is the measurement pitch, yaw and torsion as three angular rotation of controlled object. The second advantage of reflector is the measurements on the large work distances. Causes are the small value of the conversion coefficient and two orthogonal reference axes of trihedral reflector. The technical characteristics of the experimental setups of new reflector are presented. The features of trihedral reflector as the reflectors for optic-electronic autocollimators are discussed.
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