Use of elliptic functions to study skip-lock of automobile seat-belt retractors

This paper discusses the locking dynamics of automobile seat-belt retractors. The retractors considered are those having a locking bar which engages cogs when the bar is tilted by a pendulum sensing vehicle acceleration or deceleration. Conditions where a retractor may fail to lock in a timely manner are examined. It is found that such conditions can occur if the pendulum is in the neutral position (that is, out of the locking position) when the webbing unspools due to occupant movement. The pendulum can be in this out-of-locking position due to webbing slack, edge fracture of the locking bar, and pendulum rebound from oscillation. This phenomena is most likely to occur in violent accidents where occupant restraint is most needed to prevent serious injury. Elliptic functions are used to examine the pendulum dynamics. (C) 1999 Elsevier Science Ltd. All rights reserved.