By L. Huang
Statics and Dynamics of inflexible Bodies provides an interdisciplinary method of mechanical engineering via an in depth review of the statics and dynamics of inflexible our bodies, proposing a concise advent to either. This quantity bridges the distance of interdisciplinary released texts linking fields like mechatronics and robotics with multi-body dynamics on the way to supply readers with a transparent route to knowing quite a few sub-fields of mechanical engineering. third-dimensional kinematics, inflexible our bodies in planar areas and diverse vector and matrix operations are awarded with a view to offer a entire realizing of mechanics via dynamics and inflexible bodies.
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Extra resources for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
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 . The xOB axis is along the rotation axis, which is parallel to xOA . The yOB and zOB axes are perpendicular to the sides GH and EH of the rectangular box, respectively. 32 2 Kinematics zˆA zˆB β cos β β -sin β zˆA Z X O cosθ θ xˆ B kˆ sinθ -sin θ cos β yˆ A xˆ A yˆ A ˆj xˆ A OB sin β cos θ θ iˆ yˆ B Y Fig.
In this frame, the geometrical entity of the vector, a directional line, is formulated and observed by one who keeps a fixed position and orientation with respect to the frame. • The coordinate frame, called the description frame, in which the vector is described. In this frame, the directional line observed in the observation frame is presented by its projections (x, y, and z components) along the axes of the frame. In other words, a numerical or algebraic expression of the vector, a row or a column of numbers or variables, is formulated.
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. It is normally referred to as the velocity of the origin of the body frame. • Angular velocity: This refers to the angular velocity of the body around an instantaneous rotation axis.