The peg-in-hole insertion process is the most common task in the robotic/automatic assembly industry. However, the inaccuracy of the assembly robot in positioning the inserted peg into the hole due to the uncertainty of the assembly environment, represents an obstacle in this area of automation. To overcome this problem, complex and expensive equipment has been designed. The objective of this paper is to provide an in-depth understanding of the chamferless peg-hole assembly, by showing the geometrical, dynamical conditions for a successful assembly operation. Also, the results of this analysis have been simulated to demonstrate the chamferless peg-hole insertion process.