Lagrangian theoretical framework of dynamics of nonholonomic systems

By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.

Aye-aye middle finger kinematic modeling and motion tracking during tap-scanning

The aye-aye(Daubentonia madagascariensis)is a nocturnal lemur native to the island of Madagascar with a unique thin middle finger.Its slender third digit has a remarkably specific adaptation,allowing them to perform tap-scanning to locate small cavities beneath tree bark and extract wood-boring larvae from it.As an exceptional active acoustic actuator,this finger makes an aye-aye’s biological system an attractive model for pioneering Nondestructive Evaluation(NDE)methods and robotic systems.Despite the important aspects of the topic in the aye-aye’s unique foraging and its potential contribution to the engineering sensory,little is known about the mechanism and dynamics of this unique finger.This paper used a motion-tracking approach for the aye-aye’s middle finger using simultaneous video graphic capture.To mimic the motion,a two-link robot arm model is designed to reproduce the trajectory.Kinematics formulations were proposed to derive the motion of the middle finger using the Lagrangian method.In addition,a hardware model was developed to simulate the aye-aye’s finger motion.To validate the model,different motion states such as trajectory paths and joint angles,were compared.The simulation results indicate the kinematics of the model were consistent with the actual finger movement.This model is used to understand the aye-aye’s unique tap-scanning process for pioneering new tap-testing NDE strategies for various inspection applications.