By L. Huang
Statics and Dynamics of inflexible Bodies offers an interdisciplinary method of mechanical engineering via an in depth evaluate of the statics and dynamics of inflexible our bodies, providing a concise advent to either. This quantity bridges the distance of interdisciplinary released texts linking fields like mechatronics and robotics with multi-body dynamics so as to offer readers with a transparent route to figuring out a number of sub-fields of mechanical engineering. third-dimensional kinematics, inflexible our bodies in planar areas and various vector and matrix operations are awarded as a way to supply a complete figuring out of mechanics via dynamics and inflexible bodies.
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Extra info for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
3. Our task is to (1) find the position of point E and an end of edge EH of the box and (2) derive the rotational axis of frame fBg and the angular displacement of the frame around this axis with respect to the universe frame fU g W OX Y Z shown in Fig. 8. From Fig. 24). 3 Velocity In the previous sections, the methods for determining the position and orientation of a rigid body were discussed. If position and orientation change with time, two types of velocities are defined to quantify their rate of change: • Linear velocity: This is the velocity of a fixed point in a body.
Three fixed principal axes X , Y , and Z are along the base vectors iO , jO, and k. • Body frame of the rod fAg W OA xOA yOA zOA . Its origin OA coincides with O, and zOA coincides with the Z axis. The yOA axis is the projection of the rod on the XOY plane. Its angle Â with the Y axis describes the angular displacement of the rod around the Z axis. The xOA axis is then decided by the right-hand rule. • Body frame of the box fBg W OB xOB yOB zOB . Its origin OB is at the joint at the end of the rod, OB .
Step 3: Determine the linear velocity from the differentiation of position with respect to time (Sect. 3). Step 4: Determine the angular velocity from the product of the differentiation of the rotational matrix with respect to time and its transpose (Sect. 3). Step 5: Determine the linear acceleration and angular acceleration differentiating the linear and angular velocities, respectively (Sect. 4). The above steps are based on the first principle of differential relations among position, velocity, and acceleration and can be used to analyze the kinematics of rigid bodies.