Cytoplasmic dynein 1 is a dimeric motor protein that walks and transports intracellular cargos towards the minus end of microtubules. In this article we formulate, based on physical principles, a mechanical model to describe the stepping behaviour of cytoplasmic dynein walking on microtubules from the cell membrane towards the nucleus. Unlike previous studies on physical models of this nature, we base our formulation on the whole structure of cytoplasmic dynein 1 to include the temporal dynamics of the individual subunits such as the cargo (for example an endosome, vesicle or bead), two rings of six ATPase domains associated with diverse cellular activities (AAA+ rings) and the microtubule binding domains which allow dynein to bind to microtubules. This mathematical framework allows us to examine experimental observations on dynein across a wide range of different species, as well as being able to make predictions on the temporal behaviour of the individual components of dynein not currently experimentally measured. Furthermore, we extend the model framework to include backward stepping, variable step size and dwelling. The power of our model is in its predictive nature; first it reflects recent experimental observations that dynein walks on microtubules using a weakly coordinated stepping pattern with predominantly not passing steps. Second, the model predicts that interhead coordination in the ATP cycle of cytoplasmic dynein is important in order to obtain the alternating stepping patterns and long run lengths seen in experiments.