Determining and modelling the forces exerted by a trampoline suspension system

Trampolining is a sport entailing multiple somersaults and twists performed from an elastic sprung bed. During the aerial phase gravity is the only external force acting on the gymnast and since this acts through the gymnast's centre of mass, angular momentum is conserved. As somersault and twist production are an essential part of trampolining it is important to understand the mechanics for producing angular momentum during the contact phase. Previous research has neglected important factors such as the considerable mass of the bed and springs in the analysis of the contact phase. Consequently the mechanics of the contact phase is not yet clear. An experimental study is presented to determine the forces acting on the gymnast alone and the forces acting on both the gymnast and the suspension system (bed and springs) during the contact phase for plain jumps. Kinematic data was obtained using a three dimensional motion analysis system and inverse dynamics was used to determine vertical and horizontal forces. Kinetic data was recorded using four tri-axial force transducers, mounted underneath the trampoline using custom designed brackets. Peak vertical forces of 25 bodyweights were recorded during plain jumps at the centre of the trampoline and peak horizontal forces up to 0.5 bodyweights were recorded in jumps with approximately I m offorwards travel during the subsequent aerial phase. A simulation model of the trampoline suspension system was developed comprising thirty eight non-damped linear springs and fifteen point masses. The model was evaluated using experimental data of an impactor (with known mass) dropped at centre and off-centre locations on the trampoline from varying heights. Results showed the trampoline behaves as a non-linear spring. The study presents relationships between vertical force and vertical bed displacement and horizontal force and horizontal bed displacement as well as the location of the mass centre of the bed and springs as a function of the location of the bed centre. These relationships may be used to model the behaviour of the bed and springs in the analysis of the mechanics of the contact phase for trampolining skills entailing multiple somersaults and twists.