# Novel Resistive Sensor Design Utilizing the Geometric Freedom of Additive Manufacturing
## 1 Introduction  
Additive manufacturing (AM), also known as 3D printing, is a family of manufacturing processes in which parts are generated based on a 3D model, building them in a layer-by-layer fashion. Some of the most commonly applied AM processes are vat photopolymerization, powder bed fusion for polymers or metals using sintering or melting, and material extrusion (MEX) [1, 2]. Of the aforementioned, MEX has a distinct advantage when it comes to producing multi-material parts and integrated electronics, as it can easily employ multiple extruders with distinct materials. By comparison, the other commonly applied processes operate using either a fluid bath or powder bed, in which multi-material parts are difficult to realize. While it is technically possible to manufacture multi-material parts with functional electronics using AM processes other than MEX [3], the present work will focus on MEX due to its advantages in process simplicity and productivity when producing multi-material parts [4] and due to the large variety of technical and functional polymers, e.g., elastomers and electrical conductive polymers [5, 6]. Through recent advancements, it has become possible to use MEX to manufacture components from electrically conductive polymers [1, 7, 8]. Previously, indirect inclusion of conductors and sensors into AM parts had already been demonstrated, e.g., by interrupting the build to embed strain gauges [9], silver paste [10], copper wire, or copper mesh [11]. By applying conductive polymers, it has now become possible to directly include conductive traces, resistors [12], capacitors, inductors, filters [13], capacitive sensors [14, 15], piezoresistive sensors [16], thermal sensors [17], and tactile sensors [18], all within the same production process. Conductivity in the plastics is realized through the inclusion of aconductive filler within the polymer matrix. Examples of such fillers include single-wall or multi-wall carbon nanotubes (SWCNT/MWCNT), carbon back (CB), graphene, carbon fibers [19; 20], copper nanowires [21], silver nanoparticles, or combinations of different particles [22]. Table 1 provides a literature overview regarding directly produced MEX force and pressure sensors, sorting the sources by sensor working principle and the mechanical loads used to demonstrate its behavior. [PERSON] et al. [23] were amongst the first to demonstrate AM of electrically conductive polymers, using a polycaprolactone (PCL) polymer matrix with a CB conductive filler in a MEX process. The material was applied in piezoresistive flexural load sensing, capacitive detection of touch, and the detection of a fluid within a container. Although there are limitations to the work, such as a low gauge factor and a lack of in-depth consideration of the influences of sensor geometry and process parameters, it provides a proof of concept for directly manufactured AM sensors. [PERSON] et al. [7] demonstrated both a capacitive touch sensor and a piezoresistive bending sensor using acrylonitrile butadiene styrene (ABS) polymer with CB conductive particles. [PERSON] et al. [22] developed a mixture of carbon nanotubes (CNTs) and silver nanoparticles within a thermoplastic polyurethane (TPU) matrix, demonstrating its piezoresistivity under tensile load and the effects of different mixtures of the conductive fillers on the sensor behavior. [PERSON] et al. [27] demonstrated the use of polylactide (PLA) with CB to build piezoresistive sensors, and qualitatively validated their response under tensile loading. [PERSON] et al. [25] applied the same polylactide (PLA) with CB polymer to build piezoresistive sensors applied in a dynamic strain loading scenario, and their work also gave consideration to the geometric design of the strain gauges and the possibilities of improving output linearity by using two gauges. [PERSON] et al. [26] developed an ABS polymer with CNT conductive filler, and demonstrated its behavior with 0\({}^{\circ}\) and 45\({}^{\circ}\) infill and strain loading in ramp, creep, and dynamic scenarios.