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Related Concept Videos

Transformation of Plane Stress01:18

Transformation of Plane Stress

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Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
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Unsymmetric Bending - Angle of Neutral Axis01:15

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
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Angle of Twist: Problem Solving01:13

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An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the...
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Symmetric Member in Bending01:07

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In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
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A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
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Inverse solutions for tilting orthogonal double prisms.

Anhu Li, Ye Ding, Yongming Bian

    Applied Optics
    |June 13, 2014
    PubMed
    Summary

    This study presents a method for precisely directing laser beams using orthogonal prisms. The findings offer practical solutions for laser beam steering and target tracking in precision engineering applications.

    Area of Science:

    • Optics and Photonics
    • Precision Engineering
    • Robotics and Control Systems

    Background:

    • Laser beam steering is crucial for various applications, including optical sensing and manufacturing.
    • Existing methods for laser beam manipulation often face limitations in accuracy and flexibility.
    • Orthogonal prism systems offer a promising approach for precise beam control.

    Purpose of the Study:

    • To develop an analytical reverse solution for directing laser beams using orthogonal prisms.
    • To propose a numerical method for optimizing prism orientation for target tracking.
    • To demonstrate the practical applicability of the developed methods in precision engineering.

    Main Methods:

    • Derivation of an analytical reverse solution for laser beam steering.

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  • Implementation of a lookup table method for numerical reverse solution of prism tilting angles.
  • Experimental validation using case studies and an elliptical target trajectory.

    • Main Results:

    • Successful demonstration of precise laser beam direction to specified targets.
    • Effective steering of double-prism orientation for near-field target tracking.
    • Validation of theoretical derivations through case studies and trajectory scanning.

    Conclusions:

    • The analytical and numerical solutions provide a robust framework for laser beam steering with orthogonal prisms.
    • The proposed methods have significant application value in precision engineering for orientation and position tracking.
    • Further exploration of these methods can lead to advanced scanning patterns and control strategies.