Abstract: We will describe a new algorithm, which we refer to as the reflection method, to generate random walks of specified thickness in $mathbb{R}^3$ and prove that our method is ergodic. The data resulting from our implementation of this method will allows us to describe the complex relationship between the presence and nature of knotting and size, thickness and shape of the off-lattice walk. We will expand on the current understanding of excluded volume by analyzing how scaling of the squared radius of gyration is affected by the introduction of thickness. We will also examine the profound effect of thickness on knotting in open chains.