# Cardan Mechanism

## Cardan Mechanism

(also universal joint or universal coupling), a mechanism that permits rotation of two shafts at a varying angle to each other by means of a movable connection of the links (rigid Cardan mechanism) or the flexible properties of special elements (flexible Cardan mechanism). The Cardan mechanism is named for G. Cardano, who proposed a suspension for the preservation of a constant position of a body upon any rotation of its mounting.

Figure 1. Diagram of Hooke’s joint: (1) and (2) jaws; (3) spider- (8) (8’) and (C), (C) joints; (I), (II), (III), and (IV) axes of rotation

The simple rigid Cardan mechanism is called Hooke’s joint (Figure 1). The axes of rotation (I) and (II) intersect at an angle α with the fixed point O at the center of a circle of radius OB = OB’ = OC = OC’. Thus, for any value of angle ± when 0° ≤ ± < 90°, joints B, B’ and C, C’ in pairs describe the circumference of the same radius in planes perpendicular to axes (I) and (II). When these two conditions are met, the transmission of rotation with various angles a is possible. This property of a Cardan mechanism has brought about its widespread use in various machines—such as aircraft, instruments, lathes (articulated coupling), motor vehicles (Cardan drive), and agricultural machinery—that require a change in the relative position of the shafts transmitting rotation. A drawback of the single universal coupling is the nonuniformity of the speed of rotation of the driven shaft at a constant rate of the driving shaft. The change in the rate of the driven shaft increases with an increase in the angle α

Figure 2. Diagram of double Hooke’s joint: (1) driving shaft, (2) transmission shaft, (3) driven shaft, (A) and (B) universal joints

For α = 90°, transmission of rotation using a single universal coupling becomes impossible. In such cases, as well as in cases requiring uniform rotation of the driven shaft, a double universal coupling (Figure 2), in which angles ai and ±1 ±2 are equal and the jaws on shaft (2) are in the same plane, should be used. If there is insufficient space for a double universal coupling, a Cardan is used whose design is based on division of the angle between the shafts by a bisecting plane (Figure 3). The angle of inclination of the shafts of a rigid double universal coupling may reach 38°. Flexible Cardan mechanisms, with flexible elements made of a durable elastic material (Figure 4), are used for shaft angles of inclination of 3°-5°.

### REFERENCES

Mertsalov, N. I. Teoriia prostranstvennykh mekhanizmov. Moscow, 1951.
Zinov’ev, V. A. Prostranstvennye mekhanizmy s nizshimi parami. Moscow-Leningrad, 1952.
Artobolevskii, I. I. Teoriia mashin i mekhanizmov, 2nd ed. Moscow, 1967.

E. M. STARIKOV

Figure 3. Cardan mechanism whose operation is based on the priniciple of division of the angle between the shafts by a bisecting plane: (1) and (5) shafts located in the same plane and intersecting at an angle; (2) guide pin, which sets the separator upon a change in the angle between the shaft axes; (3) separtor; (4) ball bearings lying in the bisecting plane

Figure 4. Flexible Cardan mechanism: (1) centering joint pin, (2) and (4) shafts, (3) flexible elements

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