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Related Concept Videos

Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

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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...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

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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.
Here, in order to determine the magnitude of velocity and acceleration for point...
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Absolute Motion Analysis- General Plane Motion01:24

Absolute Motion Analysis- General Plane Motion

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Visualize a drone, with its propellers spinning rapidly, hovering mid-air. The fascinating movements and operations of this drone can be comprehended by applying the principle of general plane motion.
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the...
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Rotational Motion about a Fixed Axis01:26

Rotational Motion about a Fixed Axis

839
A rigid body's rotation around a fixed axis makes every point within it trace a circular path around a specific line or point. The term given to this type of spinning is defined by the angular position, symbolized by the angle θ. This angle is gauged from a static reference line to the revolving object. From this angular position, any variation is referred to as angular displacement, denoted by dθ. The extent of this displacement can be calculated in degrees, radians, or...
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Relative Motion Analysis using Rotating Axes - Acceleration01:22

Relative Motion Analysis using Rotating Axes - Acceleration

431
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.
Time differentiation is...
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Planar Rigid-Body Motion01:22

Planar Rigid-Body Motion

615
Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
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Deployable motion of rotational sliceforms.

Tim Watson1, Keith A Seffen1

  • 1Advanced Structures Group, University of Cambridge, Department of Engineering, Cambridge CB2 1PZ, United Kingdom.

Physical Review. E
|November 16, 2021
PubMed
Summary

Rotational sliceforms (RS) are novel deployable metamaterials. Symmetrical RS architectures can fully collapse, while asymmetrical ones cannot, with expansion limited to the original design configuration.

Area of Science:

  • Metamaterials Science
  • Mechanical Engineering
  • Robotics

Background:

  • Rotational sliceforms (RS) present a unique architecture of intersecting planar slices.
  • These structures exhibit inherent stiffness, self-locking capabilities, and mechanistic motion, suggesting potential as deployable metamaterials.

Purpose of the Study:

  • To investigate the natural limits of motion for both symmetrical and asymmetrical rotational sliceform architectures.
  • To understand the relationship between cell articulation range and the overall deployability of RS structures.

Main Methods:

  • Reconceptualizing RS as arrays of plane-faced pyramidal cells with rigid, zero-thickness slices.
  • Analyzing the minimum articulation range of individual cells to determine the upper bound of RS motion.

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  • Investigating slice behavior, including planar rotation limitations and out-of-plane kinking, to capture deployment dynamics.

    • Main Results:

    • The minimum articulation range of cells dictates the overall motion limits of incomplete RS.
    • Symmetrical RS architectures demonstrate full collapse capability, whereas asymmetrical ones do not.
    • Expansion of RS structures is inherently limited to their original design configuration.

    Conclusions:

    • Planar slice rotation is not feasible without distorting cell geometry; out-of-plane kinking is necessary for compatible slice rotations.
    • The analysis accurately predicts RS deployment features, including minimum collapsed states, slice deformation during rotation, and expansion limits.