Modelling a uniaxial inerter in a 2D or 3D environment: Implications of centripetal acceleration

The inerter completes the force-current analogy between mechanical and electrical components, providing equivalent to capacitor. As such, it is a two-terminal passive element that, when implemented ideally, normally said generate force proportional relative acceleration its two terminals. However, this applicable only if does not rotate, so motion device's terminals axial. In many applications, restriction acceptable, such as in car suspension systems. paper, shown that relationship terminal accelerations generated more complex used 2-dimensional (2D) or 3-dimensional (3D) environment, within multi-bar mechanism (e.g., robotic arms railway pantographs). Specifically, given by simply centripetal acceleration, resulting from rotation of inerter, needs be accounted for find second derivative length, which defines force. Two case studies are presented demonstrate effects neglected term. It an operating 2D 3D significant errors may occur evaluating also system response term neglected. Equations provided both modelling different coordinate systems incorporating multibody