An experimental apparatus was designed to test the pivoting friction moment of annular friction disc under either constant normal force and variable normal force. The experimental results demonstrated the applicability of the classical pivoting friction model under the continuous variable normal contact force, and showed that the rotary velocity affects the properties of the pivoting friction. By considering the Stribeck effect of the local friction at a contact point, a theoretical model was proposed for the pivoting friction. Good agreement between proposed theoretical and experimental results sheds light on the physical mechanism underlying the pivoting friction.

Analytical mechanics is established based on d’Almbert-Lagrange Principle, Gauss principle, Jourdian principle and Hamilton principle, to deal with the dynamics of mechanical systems subject to holonomic or nonholonomic constraints. The governing equation of the systems are derived either by introducing Lagrange’s multipliers to adjoin with the limitation equations for the virtual displacements, or by directly eliminating the constraint equations to achieve minimal formulations. The author presents a survey for the history of analytical mechanics, and explains some basic concepts, such as virtual displacement, ideal constraint, and the correlations between the Lagrange multipliers and the real constraint forces.

Nonholomonic constraints are involved for 3D point-contact problems. The virtual displacements restricted by the constraints are usually given by Appell-Chetaev’s rule. It has not been very clear of the geometric meaning in configuration space for Appell-Chetaev’s rule of nonholonomic constraints. The authors investigate point contact with pure rolling by two rigid bodies in a multibody system to discover its geometric sense. First, the sufficient and necessary conditions of point contact are given. A ball-plane system is presented to demonstrate the validation of the conditions by deducing the system’s obvious contact constraint originating from them. Two geometric restrictions for pure rolling are obtained by the nonholonomic constraints of pure rolling as well as the contact constraint in velocity level. It proves that the virtual displacements of the two restrictions are same as those of the constraints of point contact with pure rolling obtained by Appell-Chetaev’s rule. So, it is thought that the constraints of pure rolling are constructed by the two geometric restrictions.