Kinematics and mobility analysis of carton folds in packing manipulation based on the mechanism equivalent

Abstract

The process of erecting and closing a carton in packing manipulation is seen as a succession of folds in position and orientation from one distinct configuration to another. Permitted manipulations and changes in shape are governed by the geometry of crease lines, dimensions and profiles of the panels. The possibility for panels to fold into successive distinct configurations is determined by the kinematic geometry. This paper presents a mathematical basis which determines the mobility of distinct configurations of a carton to include the degrees of freedom dominating the manipulation and the overconstraint configurations in an erected and closed form, and proposes the kinematic analysis of a carton during packing manipulation. Use is made of the concept of line vectors and screw theory associated with graph theory. The analysis helps to explain some configurations which show how a carton can fold and opens up the way of describing manipulation in the packaging process.