## 1 Introduction  
A high-performance bicycle crank is considered to be one that would be installed on a racing bicycle, the elite of which are operated by professional cycling teams such as those competing in the Tour de France. There has been a considerable effort in developing an understanding of the effect of crank design on the force delivered by the rider [1; 2; 3; 4; 5], although there has been very little study of innovation of the crank design itself away from the norm [2]. This is likely in part due to lack of innovation in crank manufacturing methods. The vast majority of common crank designs are effectively box section in their form and are either machined from aluminium in halves then bonded together, or manufactured using Carbon-Fibre-Reinforced Polymer (CFRP) [6] with titanium or aluminium inserts for mechanical interfaces. These methods offer limited opportunity for design innovation.  
Component mass is a significant factor in the competitiveness of a racing bicycle and has been driven down to a low level, particularly with the incorporation of CFRP. With cranks, however, stiffness is also a major consideration in order to cycle more efficiently and effectively, maximising performance over both long and short distances through improved power transmission and reduced fatigue. These objectives are suited to topology optimisation (TO), a computer-aided design (CAD) technique. TO has been used previously for designing minimal weight structures [7; 8; 9] where low mass is critical to high component performance in the end-use application (e.g., in saving fuel [7; 9], increasing stability, and decreasing cost [8]). The effectiveness of TO techniques are often limited by conventional manufacturing techniques due to the complex natural form of the resulting geometry, making the optimal design un-manufacturable.  
Additive Manufacturing (AM) introduces an opportunity whereby this theoretically idealised geometry can be manufactured with a greater degree of economic sensibility. TO for AM has therefore become an active research area, utilizing the approach for a number of component performance objectives, such as heat transfer efficiency [10], stiffness [11], and mass [12]. A design produced using this combination of techniques could therefore exhibit maximum stiffness at a minimum mass, achieving ultimate product performance.  
The build quality of the complex geometry produced by AM, and the results of functional testing, can both be verified by using Computed Tomography (CT) scanning [13], comparing a CT-generated model with the original CAD data. A similar design investigation has been completed in the high-performance automotive sector, successfully improving the performance of engine valves by designing for AM [14].  
Application of this approach to the design and manufacture of an elite bicycle crank to obtain a combination of low mass and high stiffness has not previously been seen. This research paper demonstrates a complete workflow from design, manufacture, post-treatment, and validation of a highly loaded, spiderless, non-drive-side (NDS) crank, offering practitioners a validated approach to the application of Powder Bed Fusion (PBF) to highly loaded components.