Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and the development of treatment options imperative. The effect of motion of the coronary artery due to the motion of the myocardium is not extensively studied. In this work, we focus our investigation on the localized hemodynamic effects of dynamic changes in curvature and torsion. It is our objective to understand and reveal the mechanism by which changes in curvature and torsion contribute towards the observed wall shear stress distribution. Such adverse hemodynamic conditions could have an effect on circumferential intimal thickening. Three-dimensional spatiotemporally resolved computational fluid dynamics (CFD) simulations of pulsatile flow with moving wall boundaries were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with stationary walls is used as the baseline control case. In order to study the effect of curvature and torsion variation on local hemodynamics, this baseline model is compared to models where the curvature, torsion, and both curvature and torsion change. The simulations provided detailed information regarding the secondary flow dynamics. The results suggest that changes in curvature and torsion cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients and secondary flow patterns. The wall shear stress (WSS) varies by a maximum of 22% when the curvature changes, by 3% when the torsion changes, and by 26% when both the curvature and torsion change. The oscillatory shear stress (OSI) varies by a maximum of 24% when the curvature changes, by 4% when the torsion changes, and by 28% when both the curvature and torsion change. We demonstrate that these changes are attributed to the physical mechanism associating the secondary flow patterns to the production of vorticity (vorticity flux) due to the wall movement. The secondary flow patterns and augmented vorticity flux affect the wall shear stresses. As a result, this work reveals how changes in curvature and torsion act to modify the near wall hemodynamics of arteries.