A quick return mechanism is an apparatus that converts circular motion (rotating motion following a circular path) into reciprocating motion (repetitive back-and-forth linear motion) in presses and shaping machines, which are utilized to shape stocks of metal into flat surfaces, throughout mechanical engineering. The quick return mechanism is the foundation behind the energy of these machines.
Contents
The mechanism consists of an arm attached to a rotating disc that moves at a controlled uniform speed. Unlike the crank, the arm of the mechanism runs at a different rate than the disc. By having the disc run at a different rate than the attached arm, productivity increases because the amount of time needed for a cut is reduced. The design of this mechanism specializes in vector calculus and the physical aspects of kinematics (study of motion without the effects of forces) and dynamics (study of forces that affect motion).
History
During the early-nineteenth century, cutting methods involved hand tools and cranks, which were often lengthy in procedure. Joseph Whitworth changed this by creating the quick return mechanism in the mid-1800s. Using kinematics, he determined that the force and geometry of the rotating joint would affect the force and motion of the connected arm. From an engineering standpoint, the quick return mechanism impacted the technology of the Industrial Revolution by minimizing the duration of a full revolution, thus reducing the amount of time needed for a cut or press.
Applications
Quick return mechanisms are found throughout the engineering industry in different machines:
Design
All mechanisms are formed upon the combination of two gears, where one drives the force of the other. The disc influences the force of the arm, which makes up the frame of reference of the quick return mechanism. The frame continues to an attached rod, which is connected to the circular disc. Powered by a motor, the disc rotates and the arm follows in the same direction (linear and left-to-right, typically) but at a different speed. When the disc nears a full revolution, the arm reaches its furthest position and returns to its initial position at a quicker rate, hence its name. Throughout the cut, the arm has a constant velocity. Upon returning to its initial position after reaching its maximum horizontal displacement, the arm reaches its highest velocity.
The quick return mechanism was modeled after the crank and slider (arm), and this is present in its appearance and function; however, the crank is usually hand powered and the arm has the same rate throughout an entire revolution, whereas the arm of a quick return mechanism returns at a faster rate. The "quick return" allows for the arm to function with less energy during the cut than the initial cycle of the disc.
Specifications
When using a machine that involves this mechanism, it is very important to not force the machine into reaching its maximum stress capacity; otherwise, the machine will break. The durability of the machine is related to the size of the arm and the velocity of the disc, where the arm might not be flexible enough to handle a certain speed. Creating a graphical layout for a quick return mechanism involves all inversions and motions, which is useful in determining the dimensions for a functioning mechanism. A layout would specify the dimensions of the mechanism by highlighting each part and its interaction among the system. These interactions would include torque, force, velocity, and acceleration. By relating these concepts to their respective analyses (kinematics and dynamics), one can comprehend the effect each part has on another.
Mechanics
In order to derive the force vectors of these mechanisms, one must approach a mechanical design consisting of both kinematic and dynamic analyses.
Kinematic Analysis
Breaking the mechanism up into separate vectors and components allows us to create a kinematic analysis that can solve for the maximum velocity, acceleration, and force the mechanism is capable of in three-dimensional space. Most of the equations involved in the quick return mechanism setup originate from Hamilton's principle.
The position of the arm can be found at different times using the substitution of Euler's formula:
into the different components that have been pre-determined, according to the setup.
This substitution can solve for various radii and components of the displacement of the arm at different values. Trigonometry is needed for the complete understanding of the kinematic analyses of the mechanism, where the entire design can be transcribed onto a plane layout, highlighting all of the vector components.
An important concept for the analysis of the velocity of the disc relative to the arm is the angular velocity of the disc:
If one desires to calculate the velocity, one must derive the angles of interaction at a single moment of time, making this equation useful.
Dynamic Analysis
In addition to the kinematic analysis of a quick return mechanism, there is a dynamic analysis present. At certain lengths and attachments, the arm of the mechanism can be evaluated and then adjusted to certain preferences. For example, the differences in the forces acting upon the system at an instant can be represented by D'Alembert's principle. Depending on the structural design of the quick return mechanism, the law of cosines can be used to determine the angles and displacements of the arm. The ratio between the working stroke (engine) and the return stroke can be simplified through the manipulation of these concepts.
Despite similarities between quick return mechanisms, there are many different possibilities for the outline of all forces, speeds, lengths, motions, functions, and vectors in a mechanism.