A general nonlinear kinematic model for tape winding and its calibration

A general mathematical model is derived for the nonlinear kinematics of tape winding according to the principles of kinematics and the features of nonlinear geometries. Tape winding is a dynamical process that a tape wraps some wires in a spiral manner, which is used ubiquitously in modern industries such as aerospace, marine, automobile, and house-hold electronics. It is desirable to derive the mathematical formulae associated with the kinematics of tape winding in order to examine the specifications of wrapping products. The nonlinear mathematical relationship of time varying variables is identified through the simultaneous equations of kinematic equations and geometrical equations. It shows that the key specification of wrapping is determined by two key variables: translational velocity and angular velocity of winding. To verify the theory, we perform some experiments and extract these parameters from video images via image processing tools. The experimental results agree with the proposed theory. Therefore, the model is a proposing tool to train workers or design machines in the tape winding industries.