Final answer:
A rigid body has six degrees of freedom in 3D space: three translations (x, y, z) and three rotations (roll, pitch, yaw). Work-holding techniques must constrain all six to ensure precision. The connection between external forces and rotational motion is understood through free-body diagrams, equilibrium conditions, and the work-energy theorem.
Step-by-step explanation:
Six Degrees of Freedom of a Rigid Body
Rigid bodies in three-dimensional space have six degrees of freedom that describe their motion. These are:
- Translation along the x-axis
- Translation along the y-axis
- Translation along the z-axis
- Rotation about the x-axis (roll)
- Rotation about the y-axis (pitch)
- Rotation about the z-axis (yaw)
In work holding techniques, understanding these degrees of freedom is crucial as the goal is to control and restrict a workpiece’s movement along all six degrees to ensure precision and repeatability during manufacturing processes.
Work and Rotational Motion Relation
External forces and moments, by creating torques, affect the motion of a rigid body, altering its state of equilibrium or rotation. To analyze these effects, one must:
- Construct a free-body diagram illustrating all the forces and moments acting on the rigid body.
- Apply the conditions for equilibrium to set up equations for resolving the forces and torques.
- Use the work-energy theorem to relate the work done on a mode of rotation to the change in rotational kinetic energy.
This theorem is integral to finding the work done when a rigid body is rotated about a fixed axis, particularly pointing out that work done by a torque is equal to the change in rotational kinetic energy of the body.