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  2. Ackermann steering geometry - Wikipedia

    en.wikipedia.org/wiki/Ackermann_steering_geometry

    The Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii.

  3. Angular defect - Wikipedia

    en.wikipedia.org/wiki/Angular_defect

    Here the Gaussian curvature is concentrated at the vertices: on the faces and edges the curvature is zero (the surface is locally isometric to a Euclidean plane) and the integral of curvature at a vertex is equal to the defect there (by definition). This can be used to calculate the number V of vertices of a polyhedron by totaling the angles of ...

  4. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    Euler angles can be defined by elemental geometry or by composition of rotations (i.e. chained rotations).The geometrical definition demonstrates that three composed elemental rotations (rotations about the axes of a coordinate system) are always sufficient to reach any target frame.

  5. Piston motion equations - Wikipedia

    en.wikipedia.org/wiki/Piston_motion_equations

    For rod length 6" and crank radius 2" (as shown in the example graph below), numerically solving the acceleration zero-crossings finds the velocity maxima/minima to be at crank angles of ±73.17615°. Then, using the triangle law of sines, it is found that the rod-vertical angle is 18.60647° and the crank-rod angle is 88.21738°. Clearly, in ...

  6. Rotation formalisms in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_formalisms_in...

    The angle θ which appears in the eigenvalue expression corresponds to the angle of the Euler axis and angle representation. The eigenvector corresponding to the eigenvalue of 1 is the accompanying Euler axis, since the axis is the only (nonzero) vector which remains unchanged by left-multiplying (rotating) it with the rotation matrix.

  7. Torsion of a curve - Wikipedia

    en.wikipedia.org/wiki/Torsion_of_a_curve

    Animation of the torsion and the corresponding rotation of the binormal vector. Let r be a space curve parametrized by arc length s and with the unit tangent vector T.If the curvature κ of r at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors

  8. Degree of curvature - Wikipedia

    en.wikipedia.org/wiki/Degree_of_curvature

    The degree of curvature is defined as the central angle to the ends of an agreed length of either an arc or a chord; [1] various lengths are commonly used in different areas of practice. This angle is also the change in forward direction as that portion of the curve is traveled.

  9. Deflection (engineering) - Wikipedia

    en.wikipedia.org/wiki/Deflection_(engineering)

    It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement). A longitudinal deformation (in the direction of the axis) is called elongation . The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of ...