Dynamical analysis of machines

✍ Scribed by R. Eksergian

• Book ID: 104128283
• Publisher: Elsevier Science
• Year: 1931
• Tongue: English
• Weight: 870 KB
• Volume: 211
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(31)90442-0

✦ Synopsis

We will consider a mechanism similar to a governor linkage which is rotated about a vertical shaft with angular velocity ¢. The linkage consists of four equal bars forming a rhombus, each of length 2a and of mass m and uniformly distributed. The lower vertical joint is fixed to the shaft, while the upper vertical joint can slide freely along the shaft. The horizontal joints are connected by a spring 1 with modulus of elasticity u. The initial unstrained length of spring is 2c. The angle of any rod with respect to the vertical is 0, that is the total angle at the bottom or upper joints between the rods is 20.

The co6rdinates of the system are evidently 0 and ¢. The kinetic energy can be shown to be, T = ma2[S(sin 2 0 + ~)02 + ~ sin 2 0.62] and the potential energy due to gravity and the spring is,

The momentum corresponding to the co6rdinate 0 is

* Extension of a portion of a dissertation for the degree of doctor of philosophy submitted to Clark University, 1928.

1 Constructively, two parallel springs on either side of shaft could be used, or simply a fixed guide shaft at the top, the rotating shaft terminating at lower hinge.