High Sensitivity and Full-circle Optical Rotary Sensor for Non-cooperatively Tracing Wrist Tremor with Nanoradian Resolution

<div> <p></p><p></p><p>In this paper, a novel optical rotary sensor based on laser self-mixing interferometry is developed for the full-circle rotation measurement. The proposed sensor is convenient to use for it does not need any contact with the target or a cooperative mirror. A prototype is fabricated and tested. The measured results demonstrate a good performance compared with other optical rotary sensors, in terms of the 0.1 μrad resolution, the 2.33×10^-4 linearity and 2 μrad stability over one hour. Additionally, the repeatability error is below 14.66 mrad under 9-group full-circle tests, which exhibits the potential to be instrumentalized reliably. Error analysis and limitation discussion have been also carried out. Although the accuracy needs further improvement compared with the best rotary sensor, this method has its unique advantages of high resolution, non-cooperative target sensing and electromagnetic immunity. Hence, the proposed optical rotary sensor provides a promising alternative in precise rotation measurement, tremor tracing and nano-motion monitoring.</p><p></p><p></p></div><p></p><p>In this paper, a novel optical rotary sensor based on laser self-mixing interferometry is developed for the full-circle rotation measurement. The proposed sensor is convenient to use for it does not need any contact with the target or a cooperative mirror. A prototype is fabricated and tested. The measured results demonstrate a good performance compared with other optical rotary sensors, in terms of the 0.1 μrad resolution, the 2.33×10^-4 linearity and 2 μrad stability over one hour. Additionally, the repeatability error is below 14.66 mrad under 9-group full-circle tests, which exhibits the potential to be instrumentalized reliably. Error analysis and limitation discussion have been also carried out. Although the accuracy needs further improvement compared with the best rotary sensor, this method has its unique advantages of high resolution, non-cooperative target sensing and electromagnetic immunity. Hence, the proposed optical rotary sensor provides a promising alternative in precise rotation measurement, tremor tracing and nano-motion monitoring.</p><p></p>

High Sensitivity and Full-circle Optical Rotary Sensor for Non-cooperatively Tracing Wrist Tremor with Nanoradian Resolution

<div> <p>An optical rotary sensor based on laser self-mixing interferometry is proposed, which enables noncontact and full-circle rotation measurement of non-cooperative targets with high resolution and sensitivity. The prototype demonstrates that the resolution is 0.1μrad and the linearity is 2.33×10^-4. Stability of the prototype is 2μrad over 3600s and the repeatability error is below 0.84°under 9-gruop full-circle tests. The theoretical resolution reaches up to 16nrad. Random rotation has been successfully traced with a bionic hand to simulate the tremor process. Error analysis and limitation discussion have been also carried out in the paper. Although the accuracy needs further improvement compared with the best rotary sensor, this method has its unique advantages of non-cooperative target sensing, high sensitivity and electromagnetic immunity. Hence, the optical rotary sensor provides a promising alternative in precise rotation measurement, tremor tracing and nano-motion monitoring.</p> </div> <b><br></b>

High Sensitivity and Full-circle Optical Rotary Sensor for Non-cooperatively Tracing Wrist Tremor with Nanoradian Resolution

<div> <p>An optical rotary sensor based on laser self-mixing interferometry is proposed, which enables noncontact and full-circle rotation measurement of non-cooperative targets with high resolution and sensitivity. The prototype demonstrates that the resolution is 0.1μrad and the linearity is 2.33×10^-4. Stability of the prototype is 2μrad over 3600s and the repeatability error is below 0.84°under 9-gruop full-circle tests. The theoretical resolution reaches up to 16nrad. Random rotation has been successfully traced with a bionic hand to simulate the tremor process. Error analysis and limitation discussion have been also carried out in the paper. Although the accuracy needs further improvement compared with the best rotary sensor, this method has its unique advantages of non-cooperative target sensing, high sensitivity and electromagnetic immunity. Hence, the optical rotary sensor provides a promising alternative in precise rotation measurement, tremor tracing and nano-motion monitoring.</p> </div> <b><br></b>

High Sensitivity and Full-circle Optical Rotary Sensor for Non-cooperatively Tracing Wrist Tremor with Nanoradian Resolution

<div> <p>An optical rotary sensor based on laser self-mixing interferometry is proposed, which enables noncontact and full-circle rotation measurement of non-cooperative targets with high resolution and sensitivity. The prototype demonstrates that the resolution is 0.1μrad and the linearity is 2.33×10^-4. Stability of the prototype is 2μrad over 3600s and the repeatability error is below 0.84°under 9-gruop full-circle tests. The theoretical resolution reaches up to 16nrad. Random rotation has been successfully traced with a bionic hand to simulate the tremor process. Error analysis and limitation discussion have been also carried out in the paper. Although the accuracy needs further improvement compared with the best rotary sensor, this method has its unique advantages of non-cooperative target sensing, high sensitivity and electromagnetic immunity. Hence, the optical rotary sensor provides a promising alternative in precise rotation measurement, tremor tracing and nano-motion monitoring.</p> </div> <b><br></b>

Periodic point free homeomorphisms and irrational rotation factors

We provide a complete characterization of periodic point free homeomorphisms of the $2$ -torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$ -torus without periodic points and exhibiting uniformly bounded rotational deviations with respect to a rational direction, we show that annularity and the geometry of its non-wandering set are the only possible obstructions for the existence of an irrational circle rotation as topological factor. Through a very precise study of the dynamics of the induced $\rho $ -centralized skew-product, we extend and generalize considerably previous results of Jäger.

Surface From Circle Rotation

Descriptive geometry, as the elementary one, studies the real world by its abstractions. But Euclid’s geometry of the real world is conjugated to pseudo-Euclidean geometry, and they make a conjugated pair. As a consequence, each real figure is conjugated with some imaginary pattern. This paper apart from some science facts demonstrates the presence of imaginary patterns in geometric constructions, where the imaginary patterns manifest themselves as singularities or as geometrically imaginary points (GIP) in “Real — Imaginary” conjugate pairs. The study is conducted, as a rule, from simple to complex, from particulars to generals. Rotation of a circle around an arbitrary axis generates, in the general case, a quartic surface. Among the quartic surfaces are a circular torus and a sphere as a special case of the torus. The torus is obtained from the circle rotation around an axis lying in the circle plane. If the axis does not intersect the generating circle, then the surface is called an open torus; when the axis intersects the generating circle, then the surface is called a closed torus; when the rotation axis passes through the center of the generating circle, then the surface is a sphere. The open torus is associated with a bagel, and the closed one — with an apple. The torus is a perfect example for the application of two well-known Guldin’s formulas. Next, the imaginary torus support is considered in this paper, at the end of which the sphere and its imaginary sup - port are considered. Imaginary patterns lead to the complex numbers, in regards to which grieved the great J. Steiner, calling them "hieroglyphs of analysis". But imaginary patterns exist apart from analysis formulas — they are the part of geometry. J.V. Poncelet was the first who understood the imaginary points in 1812, being in Russian captivity in Saratov and, what is important, without analysis formulas at all. Computational geometry often shows quantities, large numbers of real figures, because it takes into account the imaginary images too.

Kinematic calibration of parallel manipulator with full-circle rotation

Purpose The purpose of this paper is to develop a means of the kinematic calibration of a parallel manipulator with full-circle rotation. Design/methodology/approach An error-mapping model based on the space vector chain is formulated and parameter identification is proposed based on double ball-bar (DBB) measurements. The measurement trajectory is determined by the motion characteristics of this mechanism and whether the error sources can be identified. Error compensation is proposed by modifying the inputs, and a two-step kinematic calibration method is implemented. Findings The simulation and experiment results show that this kinematic calibration method is effective. The DBB length errors and the position errors in the end-effector of the parallel manipulator with full-circle rotation are greatly reduced after error compensation. Originality/value By establishing the mapping relationship between measured error data and geometric error sources, the error parameters of this mechanism are identified; thus, the pose errors are unnecessary to be measured directly. The effectiveness of the kinematic calibration method is verified by computer simulation and experiment. This proposed calibration method can help the novel parallel manipulator with full-circle rotation and other similar parallel mechanisms to improve their accuracy.