Simultaneous Measurement Method and Error Analysis of Six Degrees of Freedom Motion Errors of a Rotary Axis Based on Polyhedral Prism

A novel method is proposed for measuring the six degrees-of-freedom (DOF) geometric motion errors of a rotary axis based on a polyhedral prism. An error-sensitive unit which consists of a polyhedral prism and a planar reflector, is designed to carry out measurement of all six DOF errors, including the angular positioning error, the tilt motion error around the Y axis, the tilt motion error around the X axis, the radial motion error along the X and Y axes, and the axial motion error along the Z axis. The mathematical error model, including the six DOF geometric motion errors of the rotary axis, the installation errors between the polyhedral prism and the rotary axis, the manufacturing errors of the polyhedral prism, and the position errors of the sensors, are established. The effectiveness of the proposed method and the compensation model was simulated and experimentally verified.

Barrier Options Model for Agricultural Commodity Price Protection

Application of barrier options for determining insurance premiums for agricultural commodity prices due to lower selling prices by applying certain barrier levels. In determining the price of insurance premiums for agricultural commodity prices such as rice, the price is assumed to follow the Brown Geometric Motion and for the determination of the barrier level line the researcher uses the Brown Bridge Motion so that there is a relationship between Bridge and Barrier. In conclusion, we obtain a model to determine the number of insurance premiums. The barrier option model approach is used to construct a fairer formula for insurance premiums on agricultural commodity prices.

A Method for Simultaneously Measuring 6DOF Geometric Motion Errors of Linear and Rotary Axes Using Lasers

A novel method for simultaneously directly measuring six-degrees-of-freedom (6DOF) geometric motion errors of CNC machine tools was proposed, and a corresponding measurement system was developed. This method can not only be applied for measuring a linear axis, but also for a rotary axis. A single-mode fiber was used to separate the measuring unit from the laser source in order to ensure system thermal stability and measurement accuracy. The method has the advantages of high efficiency and good accuracy, and requires no complicated decoupling calculation. The positioning error of the linear axis and radial motion error of the rotary axis are measured by laser interferometry and other 5DOF geometric motion errors by laser collimation. A series of experiments were performed to verify the feasibility and effectiveness of the developed measurement system.