In order to study the nonlinear characteristics of a mechanical dynamometer, a mathematic model is established using the
Lagrangian method. The adequate and essential conditions for homoclinic orbit and periodical orbit of the system are
discussed using the model. A bifurcation diagram of the external excitation is obtained through simulation. Simulation
results clearly show the transformation from periodic motion to chaotic motion. The system can enter the chaotic motion
through the quasi-periodic route; Poincare sections and phase portraits validate the doubling bifurcation motion of the
system. Therefore, typical nonlinear vibration can be found in this system, especially when the excitation frequency is
changing between its lower and higher values. For the purpose of improving the measuring accuracy, the parameters of
the mechanical dynamometer should be designed to keep the system in periodic and quasi-periodic motions..
The adequate and essential conditions for chaotic motions of a mechanical dynamometer with spring are studied by the
Melnikov's method. Further more, the global bifurcation diagram of the system is obtained; and the transformation
including periodic motion, jumping, doubling bifurcation motion, quasi-periodic motion, and chaotic motion. The system
could entrance the chaotic motion through the route of quasi-periodic. The system could return periodic motion from
chaotic motion by reverse bifurcation. Besides that, the bifurcation curve has the property of self-similitude.