Partially Constrained Motion

The concept of constrained motion refers to the restrictions placed on the motion of a mechanical system. In this context, the terms "incompletely constrained," "partially constrained," and "completely constrained" refer to the level of freedom of motion allowed by the system.

- Incompletely Constrained Motion: This refers to a system that has more degrees of freedom than the number of constraints applied to it. In other words, the system has excess motion that is not restricted by the constraints. The excess motion can be in any direction or rotation. It is important to note that excess motion does not necessarily mean unrestricted motion, as there may still be some restrictions applied.

- Completely Constrained Motion: This refers to a system that has the same number of degrees of freedom as the number of constraints applied to it. In this case, all motion is restricted by the constraints, leaving no excess motion. The system is fully constrained, and its motion is completely determined by the constraints.

- Partially Constrained Motion: This refers to a system that has fewer degrees of freedom than the number of constraints applied to it. The constraints limit the motion of the system, but there is still some excess motion that is not completely restricted. The system has limited freedom of motion, but not as much as in the case of incompletely constrained motion.

Now, let's apply these concepts to the given examples:

- Foot Step Bearing: A foot step bearing is a type of bearing used to support and guide the rotating shaft of a machine. It typically consists of a stationary base with a concave surface and a rotating shaft with a pointed end that rests on the concave surface. The contact between the shaft and the concave surface restricts the motion of the shaft. However, the shaft is not completely restricted and can still rotate about its axis. Therefore, the motion of the foot step bearing can be classified as partially constrained.

- Rotor of a Vertical Turbine: The rotor of a vertical turbine is the rotating component that converts the kinetic energy of the fluid (such as water or gas) into mechanical energy. The rotor is connected to the shaft and rotates about its axis. The motion of the rotor is primarily rotational, and it is constrained by the bearings and the housing. However, there may still be some small axial and radial movements allowed due to the tolerances and clearances in the system. Therefore, the motion of the rotor can also be classified as partially constrained.

In conclusion, both the foot step bearing and the rotor of a vertical turbine exhibit partially constrained motion as they have some restrictions on their motion but also allow for some degree of freedom.