5.6: Frames and Machines

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A frame or a machine is an engineering structure that that contains at least one member that is not a two-force member.

A horizontal beam is connected to a vertical beam at its left endpoint, to another vertical beam at its right endpoint, and to a diagonal beam slanting up and to the right at its midpoint. — Figure \(\PageIndex{1}\): This horizontal beam is connected to other members (where normal forces would exist) at more than two locations. This beam is therefore not a two-force member.

A horizontal beam, which has a downwards force applied at its right end, is connected at its left end to the top end of a vertical beam and at its midpoint to the bottom end of another vertical beam. — Figure \(\PageIndex{2}\): This beam has two connection points, but a force is acting on a third point. Therefore the beam has forces acting on it at more than two locations and it is not a two-force member.

A frame is a rigid structure, while a machine is not rigid. This means that no part can move relative to the other parts in a frame, while parts can move relative to one another in a machine. Though there is a difference in vocabulary in describing frames and machines, they are grouped together here because we use the same process to analyze both of these structures.

A wooden stool with a round seat on 3 legs, with each leg being connected to the two others by a single horizonal beam. — Figure \(\PageIndex{3}\): This stool contains non-two-force members (the legs) and no part can move relative to the other parts (it is rigid). Therefore it is a frame. Image by Besceh31 CC-BY-SA 2.5.

A pair of steel locking pliers. — Figure \(\PageIndex{4}\): This pair of locking pliers contains non-two-force members and has parts that can move relative to one another (it is not rigid). Therefore it is a machine. Image by Duk CC-BY-SA 3.0.

Analyzing Frames and Machines:

When we talk about analyzing frames or machines, we are usually looking to identify both the external forces acting on the structure and the internal forces acting between members within the structure.

The method we use to analyze frames and machines (no special name here) centers around the process of breaking the structure down into individual components and analyzing each component as a rigid body. Where the components are connected, Newton's Third Law states that each body will exert an equal and opposite force on the other body. Each component will be analyzed as an independent rigid body leading to equilibrium equations for each component, but because of Newton's Third Law, some unknowns may show up acting on two bodies.

Video lecture covering this section, delivered by Dr. Jacob Moore. YouTube source: https://youtu.be/QY-zWXzL7aI.