The animation shows the mechanical structure of a crank swing arm. When cycling, the crank swing arm is formed by the cyclist himself.
Note on Use
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Description of the Animation
The swing arm is formed by the cyclist’s thigh. It extends from the hip to the knee joint. A swing arm enables a swinging movement around a pivot point.
The connection between the knee joint and the pedal axle is called a linkage. A linkage is a connection between two moving parts.
The pedal lever is also referred to as a crank in this context. A crank is a component that enables rotating movement.
The static connection between the pedal axle and the hip joint is the so-called frame. The frame has a rigid structure.
The Crank Swing Arm as a Four Bar Linkage
The crank swing arm is a special case of the four bar linkage. A four bar linkage consists of four members connected by rotary joints.
Whether a four bar linkage operates as a crank rocker, double crank, or double rocker depends on the length ratios of its members. Grashof’s theorem describes this relationship: if the sum of the shortest and longest members is less than the sum of the other two members, at least one member can complete a full rotation.
In a crank rocker, the crank completes a full rotation while the rocker swings back and forth. This property makes the crank rocker one of the most widely used mechanisms in engineering.
Where Do We Encounter the Crank Swing Arm?
The bicycle is just one of many examples. The crank swing arm appears in numerous technical applications.
Windshield wipers: A motor drives a crank. Through a coupler, the rotary motion is converted into the swinging motion of the wiper arm.
Sewing machine: The rotary motion of the motor is converted into the up and down motion of the needle through a crank rocker mechanism.
Steam locomotive: The piston motion is transmitted to the wheels through a linkage system. Parts of this linkage form a crank rocker.
Oil pump (pumpjack): A motor drives a crank that moves the pump head in a rocking motion through a coupler.
Engine valve train: In combustion engines, crank rocker mechanisms control the opening and closing motion of the valves.
Kinematics of the Crank Swing Arm
As the crank rotates, the angle of the swing arm changes. This change is not uniform: the swing arm moves faster during one part of the crank rotation than during the other.
An important concept is the transmission angle. This is the angle between the coupler and the swing arm. The closer this angle is to 90 degrees, the better the force is transmitted from the coupler to the swing arm.
On a bicycle, this corresponds to the pedal position: in some positions, the rider can transfer pedaling force to the crank effectively. In other positions, the so called dead points, force transmission approaches zero. At the dead points, the crank and coupler are aligned in a straight line.
History of the Crank Swing Arm
The four bar linkage is one of the oldest mechanisms in the history of technology. Crank mechanisms were already used in antiquity for mills and water pumps.
James Watt developed a related linkage for his steam engine in the 18th century. The Watt linkage converts the linear piston motion into rotary motion. Watt himself considered this invention one of his most important.
Franz Reuleaux systematized the study of mechanisms in the 19th century. He classified the different variants of the four bar linkage and laid the foundation for modern mechanism design.
Forces and Torque
The force applied at the crank is transmitted through the coupler to the swing arm. The lever arm plays a role: the greater the distance between the point of force application and the pivot point, the greater the torque.
Torque M is calculated from force F and lever arm r:
M = F × r
On a bicycle, the lever arm is the length of the pedal crank. The pedaling force is not equally effective in every pedal position. At the top and bottom dead points, the usable torque is nearly zero because the force acts along the coupler rather than across it.
Influence of Member Lengths
The behavior of the crank swing arm depends on the lengths of the four members. Changing the ratio of crank length to rocker length alters the swing angle of the rocker.
A short crank and a long rocker produce a small swing angle. A long crank and a short rocker produce a large swing angle.
The coupler length also affects the transmission angle. Engineers choose the member lengths so that the transmission angle stays as close to 90 degrees as possible within the working range.
Comparison with Other Mechanism Types
The crank swing arm is one of several mechanism types based on the four bar linkage. The following table shows the differences:
| Mechanism Type | Input | Output | Example |
| Crank rocker | full rotation | rocking motion | Windshield wiper |
| Double crank | full rotation | full rotation | Locomotive wheels |
| Double rocker | rocking motion | rocking motion | Steering linkage |
| Slider crank | full rotation | linear motion | Piston engine |
In a double crank, both the input and output members can complete full rotations. In a double rocker, both members swing back and forth. A slider crank converts rotary motion into linear motion, as in a piston engine.
Which mechanism type is suitable depends on the desired type of motion at the output.
Overview and Download
| Title | Structure of a crank swing arm |
| Target Audience | Teachers and lecturers |
| Platforms | Microsoft® Windows® Apple® Macintosh® (version-dependent) |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | Freeware |
| Download | Contact |
Contributors
C. Hein, S. Rikowski
Sources
- Drawing based on: (http://www.erft.de/schulen/avek/Fahrrad01/fahrrad01.html (last accessed: 16 December 2011))
- Dynamic contour of the legs: http://www.kirupa.com/forum/showthread.php?279912-How-to-draw-a-border-around-movie-clip
- Authoring tool (control elements supplied): Adobe Animate
