An individual-based computational model of single-cell migration on a substrate is presented, in which the cell is represented as a tree-like network of nodes rooted at the nucleus. Nascent adhesions (N1 nodes) stochastically emerge at the periphery and mature into focal adhesions, remaining mechanically linked to the nucleus by springs whose properties evolve through exploratory, protrusive, and contractile phases, ultimately driving nucleus displacement. A secondary layer of nodes (N2), representing filopodia, extends from the adhesions and exerts outward forces through pre-tensed springs, enabling protrusion growth. This mechanical framework inherently supports mechanosensing: on soft substrates, N2 nodes retract toward N1 due to low resistance, reducing traction and limiting protrusion. The parameter space of the model was explored for a static substrate to identify key conditions enabling self-propulsion. Mechanical balance constraints delineate regions associated with either motile or stationary behavior. Within motile regimes, cell trajectories, migration speeds, and traction forces were quantified, revealing a strong dependence of migration patterns on cell morphology. Simulations reproduce a persistent random walk on a homogeneous, infinitely rigid substrate, with cells exhibiting shape fluctuations traveling longer distances than those maintaining constant morphology, which become trapped by opposing focal adhesions. This work establishes a proof of concept for a mechanistic, individual-based model that captures essential features of single-cell migration and provides a foundation for investigating the influence of dynamic substrates on cell motility.