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Relative Motion Analysis using Rotating Axes

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it...

Relative Motion Analysis using Rotating Axes - Acceleration

Relative Motion Analysis using Rotating Axes - Acceleration

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
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Relative Motion Analysis using Rotating Axes-Problem Solving

Relative Motion Analysis using Rotating Axes-Problem Solving

Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Rotational Motion about a Fixed Axis

Rotational Motion about a Fixed Axis

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One-Degree-of-Freedom System

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In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
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Relative Motion Analysis - Acceleration

Relative Motion Analysis - Acceleration

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in...

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Related Experiment Video

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Measurement of Extracellular Ion Fluxes Using the Ion-selective Self-referencing Microelectrode Technique

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Positioning Performance of a Sub-Arc-Second Micro-Drive Rotary System.

Manzhi Yang¹, Zhenyang Lv¹, Chuanwei Zhang¹

¹College of Mechanical Engineering, Xi'an University of Science and Technology, Xi'an 710054, China.

|September 28, 2021

Summary

This study presents a sub-arc-second micro-drive rotary system using a piezoelectric actuator (PZT) and a micro-rotating mechanism. The system achieves ultra-precise motion, crucial for advanced positioning and micromachining applications.

Keywords:

PZT (piezoelectric actuator)drive performance micro rotary mechanism micro-drive rotary system positioning performance sub-arc-second transformation performance

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Area of Science:

* Precision Engineering
* Mechanical Systems Design
* Nanotechnology

Background:

* Macro/micro dual-drive rotary systems require micro-drive compensation for macro-drive positioning errors.
* Achieving sub-arc-second (0.1″–1″) positioning necessitates understanding micro-drive system performance.

Purpose of the Study:

* To design and evaluate a sub-arc-second micro-drive rotary system.
* To investigate the positioning performance of a system integrating a piezoelectric actuator (PZT) and a micro-rotating mechanism.

Main Methods:

* Development of a micro-drive rotary system utilizing a PZT for ultra-high resolution linear motion (0.1 nm).
* Design of a micro-rotating mechanism based on flexible hinge principles to convert linear to rotary motion.
* Analysis of drive and transformation performance through experiments, kinematics, and simulations.

Main Results:

* The developed system provides ultra-precise rotary motion at the sub-arc-second level.
* Demonstrated good linearity of motion, essential for accurate positioning.
* Established a positioning performance equation for calculating displacements and errors.

Conclusions:

* The designed sub-arc-second micro-drive rotary system effectively achieves ultra-precise motion.
* The system holds significant reference value for ultra-precision positioning and micromachining.
* Further research on sub-arc-second rotary motion systems is supported by these findings.