This paper presents an investigation of the effects of friction stir weld tool travel angle and machine compliance on joint efficiency of butt welded 5083-H111 aluminum alloy in the presence of joint gaps. Friction stir welds are produced with a CNC mill and an industrial robot at travel angles of 1 deg, 3 deg, and 5 deg with gaps from 0 mm to 2 mm, in 0.5 mm increments. Results indicate that the more rigid mill resulted in higher joint efficiencies than the relatively compliant robot when welding gaps greater than 1 mm with a 3 deg travel angle using our test setup. The results also show that when gaps exceed 1 mm welds made with a travel (tilt) angle of 5 deg are able to generate higher joint efficiencies than welds made with a travel angle of 1 deg and 3 deg. Based on tool geometry and workpiece dimensions, a simple model is presented that is able to estimate the joint efficiency of friction stir welds as a function of gap width, travel angle, and plunge depth. This model can be used as an assistive tool in optimizing weld process parameters and tool design when welding over gaps. Experimental results show that the model is able to estimate the joint efficiency for the test cases presented in this paper.