The Practice of Engineering Dynamics. Ronald J. Anderson

Чтение книги онлайн.

Читать онлайн книгу The Practice of Engineering Dynamics - Ronald J. Anderson страница 10

The Practice of Engineering Dynamics - Ronald J. Anderson

Скачать книгу

yields,

      (1.18)equation

      This is the same result as that shown in Equation 1.13.

      The transformations described in this example are typical of those used in dynamic analysis. Dynamicists are prone to using whatever coordinate system is appropriate at the time and, sometimes, there are many intermediate coordinate systems used in deriving the final system. Nevertheless, each coordinate system in the sequence must be right handed and must be generated by a simple plane rotation from the preceding system.

Schematic illustration of a slider in a slot.

      The angular velocity of the body is not specified in magnitude but the fact that the body rotates in a plane fixes the direction of the angular velocity to be images. We assume that the angular velocity is,

equation

      where images is not constant so that images (i.e. the rate of change of magnitude of the angular velocity vector) exists.

      The position of images with respect to images is then,

equation

      and, differentiating this, we find the velocity of images with respect to images to be,

      The acceleration of the slider relative to point images is defined to be,

equation

      Since both the velocity images and the acceleration images are relative to the fixed or inertial point images, they are in fact the absolute velocity and acceleration of point images. We commonly write absolute velocities and accelerations without subscripts yielding,

      (1.21)equation

      and

      (1.22)equation

Schematic illustration of a three dimensional robot.

Скачать книгу