Grasshoff

The term "Grasshoff" refers primarily to a specific type of mechanism used in mechanical engineering, particularly in the context of four-bar linkages. A four-bar linkage consists of four rigid links connected by four joints (typically revolute or pin joints) that form a closed chain.

A Grasshoff linkage is a four-bar linkage that satisfies Grashof's Law. Grashof's Law states that for a four-bar linkage, the sum of the shortest and longest link lengths must be less than or equal to the sum of the remaining two link lengths. Mathematically:

s + l ≤ p + q

Where:

• s is the length of the shortest link
• l is the length of the longest link
• p and q are the lengths of the other two links

If this inequality holds true, then at least one link in the linkage will be capable of making a full rotation with respect to the other links. This property is crucial in many mechanical applications, as it allows for continuous rotary motion.

A linkage that does not satisfy Grashof's Law is considered a non-Grashof linkage. In non-Grashof linkages, no link can make a full rotation relative to the other links; they are limited to oscillating motions.

Within the category of Grashof linkages, further distinctions exist based on which link is the shortest and which link is fixed (the "frame" or ground link). These variations lead to different types of motion:

• Crank-Rocker: The shortest link is adjacent to the fixed link, resulting in one link (the crank) being able to fully rotate, while another link (the rocker) oscillates.

• Double-Crank (or Drag-Link): The shortest link is the fixed link, allowing both links adjacent to it to fully rotate.

• Double-Rocker: The link opposite the shortest link is the fixed link, allowing both links adjacent to the fixed link to oscillate.

The determination of whether a four-bar linkage is a Grashof linkage is a fundamental step in its design, as it directly impacts the type of motion it can produce and its suitability for various applications, such as engines, pumps, and various mechanical devices.