# Novel Resistive Sensor Design Utilizing the Geometric Freedom of Additive Manufacturing
## 1 Introduction
A further development regarding the geometry of a piezoresistive flexural load sensor was carried out by [PERSON] et al. [29], demonstrating a sensor that utilized three sense elements produced from a TPU matrix with MWCNT conductive filler. When combined, the three sense elements are intended to allow for independent detection of forces along three axes, though as noted by the authors there remains a non-negligible cross talk between the sense element signals (i.e., unwanted responses from an element on an unloaded axis). [PERSON] et al. [30] also investigated TPU with MWCNT conductive filler, exploring in depth the influences of filler concentration, build orientation, layer height, infill angle, and temperature settings during the build. Their work included the creation of a pneumatic actuator built entirely out of the conductive polymer, which showed piezoresistive sensing properties. [PERSON] et al. [14] demonstrated the use of MEX to directly manufacture capacitive force sensors from flexible TPU material with a conductive CB filler. The functionality of these sensors was demonstrated in quasi-static and sinusoidal compressive loading. Using the same TPU with CB material, a piezoresistive sensor in a bending load scenario was also demonstrated, using two mirrored sense elements to allow for improved output linearization [28], though imperfections in the mirrored set-up were reported to negatively affect the result of the linearization attempt. [PERSON] et al. [24] also investigated flexible sensors, applying a TPU matrix with MWCNT. Notably, the work includes experiments performed on various strain gauge geometries to evaluate their effectiveness. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Principle** & **Tensile Load** & **Compressive Load** & **Flexural Load** \\ \hline Capacitive & & [7; 14; 23] & \\ Piezoresistive & [16; 22; 24; 25; 26; 27] & & [7; 23; 28; 29; 30] \\ Resistive path adjustment & [31] & & [31] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of working principles and tested loads in existing literature on additive manufacturing (AM) of sensors. [PERSON] et al. [31] demonstrated a PLA matrix with conductive MWCNTs, but used a geometry designed to improve upon the low gauge factors often exhibited in AM piezoresistive sensors. This design resulted in a considerably higher gauge factor, accomplished by a resistive path that is physically lengthened under tensile or flexural loads, thereby providing an amplified response compared to the piezoresistive behavior of the material alone. Though the feasibility of AM sensors has been demonstrated, and the need to combine electronic design and printing technology acknowledged [32], only limited attempts to use AM's geometric freedom as a means of improving sensor performance have been reported. The use of a pair of AM sensors in a symmetric set-up [28] or with a gauge on the zero strain axis [25] as means of output linearization was reported, but the sense elements themselves retained a geometry similar to traditional strain gauges. In addition, the effect of different trace patterns was tested [24], but this was done largely within the confines of an essentially 2D design. Finally, the work of [PERSON] et al. [31] used the geometric freedom of AM to enable a working principle based on resistive path adjustment, but its geometry would not readily translate to compressive loads due to buckling. In summary, there is limited consideration of AM-enabled freedoms in existing sensor design, which presents an opportunity for further research. For compressive loads, the commonly used solution, as can be seen in Table 1, is a capacitive measurement. However, capacitive measurement requires more complicated circuitry than resistive measurement. This work presents a novel design for a resistive sensor for compressive loads--using the working principle of resistive path adjustment--which utilizes the multi-material properties and the geometric freedom provided by AM.