README.md

Four-bar-linkage (FFRF)

In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-chain movable linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage. Spherical and spatial four-bar linkages also exist and are used in practice [1].

These CODES are organized to represent the analysis of the mentioned mechanism, wherein the flexible behavior of its components is considered. The Equation of Motion is extended, and results are obtained with Greenwood and Augmented methods.

Results

Coordinates of the 2nd link are demonstrated in the following illustrations.

Furthermore, variation of links lengths are provided in Fig. 3.

Finally, constraint Error is depicted in the figure below .

Animation

Contact

Send any queries to Reza Nopour (rezanopour@gmail.com).

Bibliography

Hartenberg, R.S. & J. Denavit (1964) Kinematic synthesis of linkages, New York: McGraw-Hill, online link from Cornell University.

Berzeri, M. and A. Shabana (2000). "Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation." Journal of Sound and Vibration 235(4): 539-565.

Chen, X. and D.-W. Lee (2015). "A microcantilever system with slider-crank actuation mechanism." Sensors and Actuators A: Physical 226: 59-68.

De Veubeke, B. F. (1976). "The dynamics of flexible bodies." International Journal of Engineering Science 14(10): 895-913.

Escalona, J., et al. (1998). "Application of the absolute nodal co-ordinate formulation to multibody system dynamics." Journal of Sound and Vibration 214(5): 833-851.

Gloub, G. H. and C. F. Van Loan (1996). "Matrix computations." Johns Hopkins Universtiy Press, 3rd edtion.

Hartenberg, R. and J. Danavit (1964). Kinematic synthesis of linkages, New York: McGraw-Hill.

Khulief, Y. and A. Shabana (1987). "A continuous force model for the impact analysis of flexible multibody systems." Mechanism and Machine Theory 22(3): 213-224.

Shabana, A. (2020). Dynamics of multibody systems, Cambridge university press.

Shabana, A. A. (1997). "Flexible multibody dynamics: review of past and recent developments." Multibody System Dynamics 1(2): 189-222.

Song, J. O. and E. J. Haug (1980). "Dynamic analysis of planar flexible mechanisms." Computer Methods in Applied Mechanics and Engineering 24(3): 359-381.

Yakoub, R. Y. and A. A. Shabana (2001). "Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications." J. Mech. Des. 123(4): 614-621.