MagKnitic: Machine-knitted Passive and Interactive Haptic Textiles with Integrated Binary Sensing

In this paper, we introduce MagKnitic, a novel approach to integrate passive force feedback and binary sensing into fabrics via digital machine knitting. Our approach utilizes digital fabrication technology to enable haptic interfaces that are soft, flexible, lightweight, and conform to the user’s body shape. Despite these characteristics, our interfaces provide diverse, interactive, and responsive force feedback, expanding the design space for haptic experiences.MagKnitic provides scalable and customizable passive haptic sensations by utilizing the attractive force between ferromagnetic yarns and permanent magnets, both of which are seamlessly integrated into knitted fabrics. Moreover, we present a binary sensing capability based on the resistance drop resulting from the activated electrical path between the integrated magnets and ferromagnetic yarn upon direct contact. We offer parametric design templates for users to customize MagKnitic layouts and patterns. With various design layouts and combinations, MagKnitic supports passive haptics interactions of linear, polar, angular, planar, radial, and user-defined motions. We perform a technical evaluation of the passive force feedback and the binary sensing capabilities with different machine knitting layouts and patterns, embedded magnet sizes, and interaction distances. In addition, we conduct two user studies to validate the effectiveness of MagKnitic. Finally, we demonstrate various application scenarios, including wearable input interfaces, game controllers, passive VR/AR wearables, and interactive furniture coverings.


INTRODUCTION
Haptics is a critical component in designing interactive systems for tangible digital interfaces.Haptic interaction and feedback can be categorized into two primary types, active and passive.Passive haptics, in contrast to active haptics, utilizes non-powered or nonmotorized interfaces, such as physical props and textured surfaces, to provide tactile sensations to users during their active movement.These passive interfaces require minimal power consumption, have a lower cost, and are less complex to design [6].Such features make passive haptics a great ft for large-scale deployment and portable environments [40].
Conventional passive haptic devices rely on mechanical structures such as buttons, springs, and gears to generate haptic feedback.However, these devices are often rigid and infexible, which poses a challenge when integrating them with the user's body form or wearable devices.To address this challenge, researchers have been investigating new approaches to create fexible and stretchable passive haptic interfaces by leveraging soft and stretchable materials, such as elastomers and hydrogels [25].However, such soft passive haptic interfaces are usually fabricated manually with complex and time-consuming procedures.
To overcome these drawbacks, we propose MagKnitic, a novel design and fabrication pipeline for textile-based passive haptic interfaces with integrated binary sensing via digital machine knitting.Digital machine knitting is a highly versatile fabrication method that can create lightweight and stretchable fabrics with conformal shapes in a customizable, scalable, and programmable manner.Knitting is also compatible with a rich material library of functional yarns for various mechanical and electrical features.To convert users' interaction with MagKnitic as passive force feedback, we integrate commercially available permanent magnets and ferromagnetic yarns into fabrics by digital machine knitting seamlessly.Our approach expands the design space for haptic experiences through digital fabrication technology, enabling haptic interfaces that are soft, lightweight, and conform to the user's body shape while providing strong, interactive, and responsive force feedback.
MagKnitic supports fully programmable and customizable designs, which enable precise control of the placement and density of the magnets and ferromagnetic yarns within the fabric through a parametric design pipeline.Six design templates for passive haptic interactions enable fast prototyping, including linear, polar, angular, planar, radial, and free motions.In addition, MagKnitic enables further programming of passive force sensations through post-fabrication techniques such as embroidering and altering the arrangement of the permanent magnets.This feature provides a high degree of customization and adaptability, allowing users to fne-tune the haptic feedback to their specifc needs and preferences.In addition to providing passive force feedback, MagKnitic can also integrate resistive binary sensing capability via the high conductivity of integrated ferromagnetic yarn and permanent magnets.Such a sensing mechanism works in tandem with the passive force feedback generation, enabling interface designs with both input and output capabilities.
In this paper, we contribute the following: • A programmable fabrication pipeline for textile-based passive haptic interfaces with integrated resistive binary sensing capability using industrial digital knitting machine and commercially available functional yarns.• Interactive parametric design templates for fast prototyping and customization on designs, enabling passive force feedback for linear, polar, angular, planar, radial, and free interactions, as well as binary sensing capability.• Technical evaluations on passive haptic feedback and sensing capability of MagKnitic with diferent ferromagnetic knitted patterns and layouts.
• Preliminary user studies on the efectiveness of MagKnitic for the passive haptics feedback.• Demonstrations of various MagKnitic prototypes across diverse interactive application scenarios.

RELATED WORK
We briefy review related works on passive haptics, machine-knitted smart textiles, as well as magnetic interactions in HCI.

Passive Haptics
Passive haptics provides users with indirect feedback about their interactions with virtual objects, with the use of non-powered or non-motorized devices [6].Traditionally, passive haptics feedback is generated by rigid mechanical structures, such as buttons, springs, and joysticks, as well as material-specifc properties that can dissipate and redirect forces during interactions, like elastic and magnetic materials [18].Researchers have explored integrating structure-driven approaches with various devices and interfaces, such as MagGetz [8] and shiftIO [42] for mobile phones, and FlexMarker [43] for interactive surfaces.Another commonly employed approach that leverages structure-driven design is based on Origami and kirigami-based structures.For example, Foldio [33] and Sensing Kirigami [56] provided binary haptics feedback with foldable paper structures, and Kirigami Haptic Swatches [4] further enabled quantitatively adjustable passive haptics feedbacks of four types of kirigami buttons.For materialdriven passive haptics, Ogata et al. implemented linear and planar feedbacks with embedded permanent magnets [31,32], Yasu et al. also worked on multiple projects utilizing magnetic rubber sheets, including rubbing over [48] or overlaying one or multiple magnetic sheets [49,50], for passive haptics over 2D surfaces.More recently, with the development of rapid prototype techniques like 3D printers, functional inkjet printing and computational knitting machines, complicated structures with integrated electronic functions became easier to design and fabricate [58,59], along with newly available materials, which led to advances in both structure-driven and material-driven passive haptics feedback design.For instance, with structure-driven passive haptics, FlexHaptics [19] introduced passive haptic input interfaces utilizing planar compliant structures, Shape-Haptics [57] investigated planar & passive haptics feedback with "click" structures, and Ondulé [7] with spring structures.Rivera et al. and Ion et al. expanded on material-driven approaches, with embedded elastic textiles [39] and 3d printable metamaterials [9], respectively.The afordances of surface gestures and passive haptics on diverse textile user interfaces have also been investigated [21,28,34].
Inspired by both structure-driven (i.e.programmable knitting structures) and material-driven (i.e.ferromagnetic & conductive yarns) approaches, we propose MagKnitic, a novel textile-based passive haptic interfaces integrated binary sensing via a highlycustomizable digital fabrication technique, digital machine knitting.

Machine-knitted Smart Textiles
Digital machine knitting is a widely used textile manufacturing method that enables the automated and programmable production of textiles by creating interlocked-loop structures (stitches).Knitted textiles possess desirable attributes such as softness, fexibility, and conformability.In this work, all samples are fabricated using a v-bed weft digital knitting machine.The machine comprised a front and a back needle bed.By utilizing combinations of various needle operations such as knits, transfers, and tucks, digital knitting machines allow for the customization of textiles with unique features such as color, texture, pattern, and properties [45].
Advances in computational design tools for digital machine knitting promote an accessible, interactive, and rapid design process.McCann et al. [27] introduced Knitout [26], a compiler that translates high-level shape primitives into low-level knitting machine instructions.This design pipeline was subsequently expanded to an interactive design interface [51].Similarly, based on high-level primitives, Kaspar et al. [11,13] introduced an interactive web-based knitting design interface.[52] introduced the stitch meshes framework, which built yarn-level models and served as an efective 3D design and modeling interface for editing at the stitch level.Such frameworks were later applied to machine knitting design [29,47].The design process could be further expedited by a machine learningbased pipeline [12], which converted visual patterns into low-level knitting instructions.We leveraged Knitout compiler for the interactive designs of MagKnitic.
Sensing capabilities can be seamlessly integrated into textiles by digital machine knitting through the integration of functional materials.Full-sized knitted garments such as socks, vests, and gloves with embedded resistive pressure sensing matrices were presented through the scalable and seamless integration of coaxial piezoresistive fbers using a digital knitting machine.This integration enables real-time human-environment interactions and human-robot interactions [22,60].Similarly, Wicaksono et al. [46] demonstrated the use of knitted conductive traces as electrodes for resistive sensing matrices and presented activity recognition and monitoring through knitted tactile sensing socks and carpets.Leveraging the unique geometries and structures of the knitted textiles, conductive yarns were also integrated into knitted textiles by plating and short-rows to enable resistive and capacitive sensing for programmable interactive user interfaces [23,35].Aigner et al. [1] stepped further to integrate piezoresistive yarn as a spacer through digital machine knitting for continuous pressure sensing.
Previous works have also demonstrated actuation in knitted textiles for assistive wearables, interactive user interfaces, and soft robotics.Albaugh et al. [2] leveraged the knitting technique of inlaying, where a yarn was inserted across the knitting structure as the cable for actuation.Actuation was also performed in knitted textiles through memory alloy, which was seamlessly integrated into the knitted fabric and generated deformation during heating [5,15].Coupling with a pneumatic system, Luo et al. [24] leveraged the anisotropic behaviors of knitting covers, which constrain the motion of tubular objects as pre-defned and induce bending-based deformation.Similarly, integrating fuidic fbers into knitted textiles enables dynamic motion through pneumatic actuation [14,16].
Harnessing the programmable and customizable properties of digital machine knitting, as well as its compatibility with a diverse range of materials, we seamlessly integrate passive force feedback with binary sensing into textiles.Our approach is both scalable and cost-efective while remaining highly portable.

Magnetic Interactions in HCI
There are three types of magnets: permanent magnets, temporary magnets, and electromagnets [20].Permanent magnets emit a magnetic feld without the need for any external source of magnetism or electrical power.Temporary magnets, also with no external power needed, behave as magnets only while near something that emits a magnetic feld and lose these characteristics when the magnetic feld is removed.Electromagnets, on the other hand, require electrical power in order to behave as a magnet.Magnetic interactions generated by these three types of the magnets, individually or in combinations, have been explored in various HCI applications, including wearable haptic feedback, interactive displays, and physical inputs.Electromagnets, for example, have been used for generating dynamic and wearable haptic feedbacks [36], tangible displays [3,38,53], as well as fabricating programmable interfaces when combined with permanent magnets matrices [30] Permanent magnets, including soft magnets and magnetic sheets, have also been explored for haptic feedback [25,49,50] and macrotexture designs [48].More recently, researchers have investigated integrating magnets to 3D printed objects, combined with electromagnets and temporary magnets, for making 3D printed objects interactive [37], providing force feedbacks [31,55], objects assembly [44], and electronic prototyping [41].Furthermore, magnetic force feedback has been studied computationally [32], which allows for the design of magnetic force feedback based on user-defned parameters.
MagKnitic utilizes the strong magnetic feld generated by permanent magnets, and integrates with highly versatile machine knittable temporary magnets (i.e.ferromagnetic yarn), which results in a a customizable, scalable, and programmable haptic interfaces with high force-to-weight ratio.We choose permanent magnet over electromagnet because embedded permanent magnet has higher magnetic fux per square unit on textiles compared to embroidered copper coils, and is safer and more comfortable for users (no external electrical power and no additional current-generating hardware).

MAGKNITIC 3.1 Principle
The passive force feedback in MagKnitic was generated through the interaction between permanent magnets and ferromagnetic yarns.The ferromagnetic yarn (Filix) is made of stainless steel fber, which comprises iron and exhibits the unique ability to interact with a magnetic feld and get magnetized.A typical passive haptic unit is made of knitted fabric with plated ferromagnetic patches and another knitted fabric with a split pocket for the permanent commercial magnet (K&J, Neodymium, N52, axially magnetized) insertion.When the permanent magnet approaches a knitted fabric integrated with ferromagnetic yarn caused by a human's motion, an attractive force between two pieces of fabric is generated and transmitted to the user through the fabric, providing them with customized feedback (Figure 2 left).Our force feedback mechanism operates with zero energy consumption.Unlike active haptics, our passive haptic design eliminates wiring, batteries, and driving circuits.This not only conserves energy, but also facilitates seamless integration into wearable devices, enabling unobtrusive passive force feedback during user interactions.
We further augment MagKnitic with a binary sensing capability by utilizing the high conductivity of ferromagnetic yarn and the Thanks to the high conductivity of permanent magnet and ferromagnetic yarn, as the user's motion brings the plated conductive pocket with inserted magnet into contact with the integrated ferromagnetic yarn, active electrical paths form and the measured resistance signifcantly drops, enabling binary sensing on the user's interaction accompanied by the passive haptic feedback to the user.
permanent magnet.We achieve this by placing the permanent magnet in a split pocket plated with conductive yarn (Figure 2 right).As the user brings the pocket with inserted magnet into direct contact with the ferromagnetic patch, the resistance drops signifcantly due to the activated electrical paths.This drop in resistance allows us to detect the presence of user motion or interaction by measuring the resistance between the knitted pocket with inserted magnet and the integrated ferromagnetic patches.In this work, we focus on passive force feedback that provides a single instantaneous response to the user upon interaction with the interface.Therefore, binary sensing, which detects the presence or absence of interaction, is preferable over continuous monitoring of the applied force level.Note, unlike passive haptic, power supply is needed for sensing signal serialization and visualization.

Designs for Various Motions
Inspired by previous works on magnet-based passive haptic interactions [55], we propose designs for six diferent passive haptic interactions that involve linear, polar, angular, planar, radial, and free motions (Figure 3).Here, we describe their interaction principle and how we leverage machine knitting to fabricate them.
Linear motion.Interacting with linear motion involves pushing or pulling along a straight path, which was often implemented as a slider.MagKnitic featuring passive force feedback during linear motion is knitted as a fat sheet, with plated ferromagnetic patches and a split pocket for magnet placement in a linear arrangement.
Polar motion.Interacting with polar motion involves spinning or rotating around a fxed point or axis, which was often implemented as a knob.MagKnitic featuring passive force feedback during polar motion is implemented as a double sheet structure by knitting on both the front and back beds.The front sheet obtains a split pocket for magnet placement, and the back sheet obtains plated ferromagnetic patches at desired locations.The two knits are interconnected by transferring two stitches at the center from the front bed to the back bed, which serves as the spinning fxed axial point.
Angular motion.Interacting with angular motion involves fipping around an axis within a two-dimensional plane, which was often implemented as a switch.MagKnitic featuring passive force feedback during polar motion is fabricated by knitting on both beds.The outof-plane fipping patch with the split pocket for magnet placement is knitted on the front bed, while the base structure with plated ferromagnetic patches is knitted on the back bed.All stitches from the front knitted fipping patch is transferred and merged to the base structure on the back bed.The merged seam serves as the fipping axis.The integrated ferromagnetic patches are arranged linearly and separated by the merged seam of the fipping patch, ofering passive force feedback during the angular fipping interactions.
Planar motion.Interacting with planar motion involves panning along a two-dimensional plane, often implemented as a thumbstick interface.MagKnitic featuring passive force feedback during planar motion is based on tubular knitting with an enclosed bottom and top.During tubular knitting, stitches are made across both the front and back beds.The split pocket is integrated into the front knits, and the plated ferromagnetic patches are integrated into the back knits at desired locations.Note that the tubular knitted structures as the essential shape primitive of knitting is also supported by our planar motion intersection.In that case, two encased tubes can move freely along the axis direction and rotate to enable the passive haptic feedback.
Radial motion.Interacting with radial motion involves adjusting the angle and direction along a circular path with the combination of rotating and fipping motion, often implemented as a joystick.MagKnitic featuring passive force feedback during radial motion obtains similar designs to the one featuring angular motion.The radial patch with the split pocket for magnet placement is knitted on the front bed, while the base structure with plated ferromagnetic patches is knitted on the back bed.Stitches from the front knitted radial patch frst decrease into two stitches and are transferred and merged to the base structure on the back bed.Since there are only a few interconnected stitches, the out-of-plane knit could be fipped and rotated, enabling radial interactions.
Free motion.Interacting with free motion involves controlling the movement in a three-dimensional space.MagKnitic featuring passive force feedback during radial motion is enabled with two separated fabrics, one fat sheet with plated ferromagnetic patches knitted on the front bed and another fat sheet or tubular structure with split pockets for magnet placement.
MagKnitic ofers passive haptic feedback for each interaction through the machine-knitted textile interface without requiring any external power source or electronic components, allowing for accessible, natural, and comfortable user input, control, and interactions.

Parametric Templates
We ofer interactive parametric design templates for MagKnitic designs featuring passive haptic feedback during each interaction.Our design templates are compiled and visualized based on .Knitout [26,51].Figure 4 shows an example template on a design enabling angular interaction.Users can defne various parameters, including which yarn carrier to use, with or without the integration of conductive yarns for binary sensing, the size of the base structure, the placement of ferromagnetic patches, and so on.Our templates take all user-defned parameters to the .Knitout compiler, which outputs the corresponding low-level machine instructions (.DAT fles).
The digital knitting machine is able to fabricate the defned designs automatically after importing the output machine instructions.All templates can be found in Supplementary Materials.

Fabrication
MagKnitic can be fabricated automatically using a digital machine knitting (Shima Seiki SWG091N2G, 14 gauge).The digital knitting machine comprises a front and a back needle back (Figure 5), which enables the fabricating of full-sized garments, e.g., socks, and gloves in a single machine run.Fabrics of diferent geometries, patterns, and textures are generated using the diferent operations of needles, including knits, purls, tucks, and so on.The fabrication of MagKnitic leverages the knitting technique of splitting and plating.Splitting is a technique to extend a second sheet from the base sheet.This technique creates pockets or separates fabric sections from the base designs.Plating is a technique of using two diferent yarns together in the knitting process to create a single layer of fabric.In plating, one yarn is knitted on the front of the fabric, while the other is knitted on the back.Plating can combine diferent colors or properties in a single layer of fabric.We use 1-ply acrylic knitting yarn (Uppingham) for the base structures, stainless steel yarn (Filix) as ferromagnetic yarn and polyester yarn with 20% micro stainless steel fber as conductive yarn.All samples are knitted using half-gauge, meaning every other needle is used during the knitting.
Conductive pocket for magnet placement.A pocket for permanent magnet placement can be created by splitting a second knitted layer from one side of the needle bed at specifc locations.This is achieved with a sequence of transferring and tucking.To further enable binary sensing, conductive yarn is integrated into the split pocket by plating (Figure 6 left).
Ferromagnetic patch.The ferromagnetic yarn is compatible with all needle operations so can be knitted, plated, transferred, and inlaid by the industrial knitting machine.The ferromagnetic patches are incorporated into the knitted fabric at predetermined locations by plating the ferromagnetic yarn with the standard acrylic knitting yarn at specifc needles (Figure 6 right).
After the samples are knitted, we manually place the commercial permanent magnets into the corresponding knitted pocket.To enable binary sensing, electrical connections are established by entangling read-out cables with the plated conductive yarns in the split pocket and the ferromagnetic patch.

TECHNICAL EVALUATION 4.1 Passive Force Feedback
The passive haptic feedback is afected by both the amount of integrated ferromagnetic yarn, which varies based on the knitting designs, and the magnitude of the applied magnetic feld, which is determined mainly by the size of the integrated permanent magnet.We characterized the efectiveness of various knitting patterns by approximating the force generated between knitted ferromagnetic patches with varying designs and a fxed magnet.The measurement was done on a customized mechanical testing setup, where a permanent magnet was fxed on the bottom plate integrated with a load cell, and the ferromagnetic knitted patches were fxed on the top plate.The top plate can move vertically, where the distance between the two plates and the reading from the load cells can be recorded simultaneously (Figure 7 left).As demonstrated in Figure 8, patterns with higher ferromagnetic yarn compositions, such as seed, knit with tucks, and jacquard knits, obtain steeper force response curves, indicating stronger force feedback.On the other hand, the quarter gauge knit obtains the weakest force response due to its lower ferromagnetic yarn composition.In this work, we opt for a stronger force response; to further optimize for the knitting complexity, we select seeds for most of our ferromagnetic patch designs.Figure 9 shows the force response between a plated ferromagnetic patch and permanent magnets of diferent sizes (diameters of 1/4", 1/2", and 1", the thickness of 1/16").A larger magnet generates a stronger force response due to the introduction of a stronger magnetic feld.However, we also note that larger magnets are heavier, which must be taken into consideration for real-life applications.
Moreover, we evaluated the dynamic force responses of MagKnitic during coaxial interaction.The characterization was performed on a similar setup with a single or an array of permanent magnets fxed on a bottom plate with an integrated load cell and the knitted ferromagnetic textiles fxed on the top plate.The top plate can be moved horizontally (Figure 7 right).We measured the force response curves from a knitted fabric with patterned ferromagnetic patches as it moved horizontally across a fxed magnet (Figure 10), as well as the force response curves from a single knitted ferromagnetic  patch moving horizontally across a defned magnet array (Figure 11).Diverse force characteristics can be obtained by varying arrangements of the plated ferromagnetic patch or the inserted permanent magnets, demonstrating possibilities for creating a wide range of passive haptic sensations and force feedback using our approach.

Binary Sensing
Within the context of passive interactive haptics, we specifcally focus on binary sensing in this work.Coupling passive haptic feedback with binary sensing, which enables the detection of the presence or absence of an interaction, we are able to create a more sophisticated and versatile interactive system.We evaluated the binary sensing performance with diferent commercial conductive yarns, including ferromagnetic yarn (50 Ω/m), polyester yarn with 20% dispersed stainless steel fber (4000 Ω/m), and silk yarn with intertwined single stainless steel thread (700 Ω/m).
To quantify the performance, we focused on the angular interaction mode.The out-of-plane fipping knits were machine-knitted using three diferent conductive yarns in pure or plated designs.Resistance was measured between the fipping knits with inserted permanent magnet and the ferromagnetic patch during the characterization.The resistance is overloaded when the fipping knits are not in contact with the ferromagnetic.On the other hand, when the fipping knits come into contact with the ferromagnetic patch during the angular interactions, the measured resistance drops dramatically due to the formed electrical paths (Figure 12).Compared with designs made of plated conductive yarn, designs with pure conductive knits enable larger contact areas for electrical paths and hence obtain lower resistance during the interaction.Since ferromagnetic yarn has the lowest resistance, designs made of ferromagnetic yarn obtain the lowest resistance when the interaction occurs.It is also interesting to note that designs with plated silk-based conductive yarns are overloaded  during the interactions; this is because the intertwined structure in silk-based conductive yarn and the plating structure limit the exposed area of the conductive stainless steel thread and restricts the stable electrical interactions between the fipping knits and ferromagnetic passive haptic patches.
In this work, we select plated polyester yarn with 20% dispersed stainless steel fber (design #4).Its distinct change in resistance range (overload to kΩ range) makes it efective for binary sensing.Additionally, unlike ferromagnetic yarn, the polyester-based yarn does not interfere with the designed passive force feedback.Moreover, plating is a straightforward technique for integrating functional yarn into textiles, which made it a practical choice for our implementation.

APPLICATION
Thanks to the digital design and fabrication pipeline, we are able to integrate MagKnitic into textiles spanning from compact wearables to full-sized furniture coverings and carpets in a seamless and salable manner.In this section, we discuss applications of MagKnitic in passive yet interactive textile-based input wearables, soft game controllers, and large-scale objects like furniture coverings.All examples are built with our parametric design templates and fabricated in one go.

Input Wearables
MagKnitic is uniquely suitable for integration into full-sized garments due to its compatibility with the industrial textile manufacturing process.As demonstrated in Figure 13, wristbands embedded with MagKnitic enable angular and polar interactions, which can serve as a customizable fip and rotary interface for wearable devices, such as for mode switch controls (focus, driving modes etc.) on mobile devices.
Coupling with binary sensing, MagKnitic ofers solutions for wearable input interfaces with programmable haptic feedback.For example, we developed a custom text input device in the form of a glove (Figure 14).The digitally knitted glove includes 10 ferromagnetic patches along the index, middle, ring, and pinky fngers, as well as a conductive pocket with an embedded magnet on the thumb.Each of the ferromagnetic patches is designed as one key of the T9 predictive text input, plus one patch for the space & delete key.Together it can serve as a wearable keypad for user input.The user can perform input by getting the thumb tips towards a specifc ferromagnetic patch, which causes the resistance to drop dramatically between the pocket and the patch, indicating the press input from the user.At the same time, the user receives haptic feedback through the generated attractive force as a confrmation of successful recordings of the input.
This setup can also be incorporated similarly into a sleeve and a hat with various ferromagnetic patch layouts as wearable shape input or music control interfaces for mobile devices (Figure 15).By wearing a glove with a conductive pocket for an embedded magnet at the index fngertip, users will be able to input commands through diferent fnger movements while perceiving tactile feedback that enhances their experience with the wearable input interface.These eyes-free interactions [10,54] can be important for safety and convenience in various situations.For example, users can control their music or make phone calls while they are driving or walking in the street.

Soft Game Controller
To demonstrate MagKnitic's capability for planar interactions, we implement a textile-based thumbstick-like game controller interface (Figure 16).This soft custom controller is designed for adolescents or users with small hands, for whom the conventional game controllers are too big.Integrated with four ferromagnetic patches, this soft and fexible controller enables binary directional sensing, allowing users to input through planar motion.In addition, it provides passive haptic feedback that enhances the users' sense of immersion during their planar interaction.

Furniture Coverings
Unlike traditional passive haptic technologies that require rigid mechanical components and are challenging to be scaled up, MagKnitic can be seamlessly integrated into large-scale objects, such as furniture coverings.For example, it could be used to create interactive tablecloths and sofa coverings (Figure 17) that provide users with both comfort and aesthetic appeal and an immersive and tactile user interface with passive haptic feedback.

PRELIMINARY USER EVALUATION
In this section, we discuss preliminary user evaluation on MagKnitic, with two user studies on the efectiveness of the generated passive haptic feedback.Both studies are evaluated and approved by The Committee on the Use of Humans as Experimental Subjects of our institute.

User Study #1
In our frst user study, we investigated the efectiveness of our passive haptic feedback by evaluating users' perceptions toward diverse force feedback characteristics generated by MagKnitic.
Study procedure.During the study, participants wore a machineknitted glove with an integrated ferromagnetic patch at the index fngertip.Participants frst got the opportunity to experience the passive haptic feedback generated via MagKnitic by approaching a permanent magnet.Then, they were asked to identify the predefned 9 textured surfaces by hovering their index fngertip above diferent permanent magnet layouts.The magnet layouts varied in each magnet's magnetic fux density and spacing, which were expected to create diferent force curves during the participant's fnger movement.A piece of paper was placed on top of the magnet layouts so they were invisible to the participants.Participants were free to interact with the surface until they were confdent about their answers.We recorded the participants' answers once they confrmed their selections.
Results. Figure 18 demonstrated the confusion matrix depicting the identifcation of experienced force curves by participants, which were generated by diferent magnet layouts.In general, participants achieved 93.1% accuracy in identifying the textured surfaces.Accuracy is almost perfect except for designs #3 and #9.This suggests that users had a distinct perception of the presence of passive force feedback, the spacing between every single peak of the provided force feedback, and the intensity of the force feedback when a reference was provided (i.e., when both the strong and weak feedback were provided).

User Study #2
In this user study, we investigated the efectiveness of MagKnitic for user input.
Study procedure.In this study, the participants were asked to interact with a swatch enabling polar interactions.The swatch was integrated with two ferromagnetic patches at the bottom layer and a pocket for permanent magnet insertion at the top.Before the study, we let the participants experience the generated haptic feedback when they rotated the top layer.During the study, the participants were asked to rotate the top layer 30, 60, 90, 120, and 150 degrees, respectively, to the target position, where the integrated ferromagnetic patch was located.The same procedure was performed both with and without the permanent magnet inserted to provide haptic feedback.Participants were free to interact with the swatch until they felt confdent that they had rotated to the target position.We  recorded the time each participant took to complete the task and their accuracy.
Results.Overall, participants reported experiencing higher resistance during rotation when the inserted magnet aligned with the ferromagnetic patches.As shown in Figure 19, the integration of passive force feedback results in higher accuracy on the rotation task.This is because the passive force feedback gave users a tactile cue to indicate whether they were reaching the target position.It is also noted that in the absence of integrated force feedback, participants achieved the highest accuracy when performing 90-degree rotations.This is because the 90-degree rotation is a more familiar and intuitive task for the participants.We have also observed that, on average, it takes users a long time to complete the rotation.However, 2 out of 6 participants performed the rotation faster when passive force feedback was not integrated.According to the 2 participants, without integrated force feedback, they lacked a means of determining whether their actions were correct.Consequently, they had to perform the task randomly, which may be efcient but not accurate.
The high accuracy exhibited by users in distinguishing between various force feedback characteristics and the improved accuracy observed in rotation tasks confrms the efectiveness and capability of MagKnitic, reiterating its potential for real-world applications.

DISCUSSION 7.1 Use of Permanent Magnets
In this work, we used permanent magnets rather than electromagnets to provide a magnetic feld for force feedback due to several reasons.First of all, conventional electromagnets are based on coil structures, which are not feasible through digital machine knitting.While electromagnets are feasible through digital embroidery, another scalable textile manufacturing technique (Figure 20), the magnetic fux generated by an embroidered electromagnet powered by a 3.7 V battery is more than 1000 times weaker than that produced by a permanent magnet of the same size.Additionally, although electromagnets ofer the advantage of programmable and active haptic feedback, they also raise concerns about safety due to the current and generated heat.They are also subject to signifcant energy consumption.These limitations make textile-based electromagnets less practical for wearable applications.
Taking into account the constraints of electromagnets in textilebased wearable applications, we opted to use permanent magnets for their simplicity, reliability, and energy efciency.Our integrated permanent magnets are comparable in size to rigid buttons and zippers commonly found on garments (radius < 1/2" and thickness < 1/16").Despite adding a non-textile-based component to the systems, the small permanent magnets provide a strong and constant magnetic feld without adding signifcant stifness to the textile substrate.In the future, we also plan to explore the integration of polymer-based magnets [25] with textiles to enable a fully soft interface.

Potential Applications in Virtual Texture Rendering
Passive haptic provides a natural and comfortable experience for VR/AR applications while keeping the cost and complexity of the device at a minimum.We propose potential applications of MagKnitic as easily integrated into AR/VR wearables, providing a subtle and realistic tactile sensation to the user and enhancing the sense of presence and immersion in the virtual environment in a passive manner.For instance, by wearing the socks and stepping towards a foor area or a knitted carpet with embedded magnets arrays, users will experience the sensation of walking on the muddy wetland, feeling the resistance and texture of the surface (Figure 21 bottom).
Similarly, wearing the gloves and moving across a magnet array, users will experience touching a rough stone surface and feeling the bumps and irregularities of the texture (Figure 21 top).As demonstrated in preliminary user evaluation, our passive haptic feedback allows the user to feel the diferences between various magnet layouts and magnetic fux densities, which demonstrate potential for embodying diferent textures in VR, e.g.mudding wetland, clean trial, and rough stone surface, in a soft, fexible, conformal, and natural form factor.
More user studies will be planned to validate users' sensation over MagKnitic in VR environments.

Limitations
MagKnitic is a passive interface that benefts from being scalable, portable, low-cost, and low-power.However, it also sufers from common limitations of passive haptics, the lack of specifcity and real-time response.MagKnitic needs to be pre-programmed and does not respond to real-time changes.This may limit the realism and efectiveness of the haptic feedback in high-speed or unpredictable environments, especially for AR/VR applications.Also, because ferromagnetic materials can only be attracted to the magnetic feld, MagKnitic can only utilize the attractive force between the ferromagnetic yarn and magnet.This means that the system is limited to providing passive haptic feedback in a single direction, namely towards the magnet.While this may be sufcient for most applications for tangible user interfaces, it may not be ideal for more complex interactions that require feedback in multiple directions.Also, the spatial resolution of passive haptic units and binary sensors are inherently constrained by the resolution of knitting structures.

Future Work
Our approach can be extended to a bigger design space and even to active haptics.With the fast advances in materials science, we speculate the possibility of integrating programmable magnetic materials into fbers or textiles.This will introduce both attractive and repulsive force responses to the current system and expand the design space.Additionally, we plan to investigate the integration of miniaturized electro-permanent magnet systems [17], which could transform our system into an active haptics system capable of real-time interactivity and programmable active haptic responses.Extending or combining the current fabrication pipeline to diferent textile manufacturing methods, such as weaving and embroidery, is also an interesting avenue for future research.
Although MagKnitic supports various passive haptic interactions, we have not verifed whether users can distinguish these haptics.We plan to conduct comprehensive user studies to validate users' perception during their interactions with various MagKnitic designs, which will help us further explore the potential applications of our passive haptic designs.

CONCLUSION
We present MagKnitic, which integrates passive force feedback and resistive sensing into fabrics via digital machine knitting.With its soft, fexible, and lightweight nature, MagKnitic conforms to the human body and provides unique and natural tactile sensations, as well as perceivable haptic feedback during users' interactions and motions.Coupling with the complementary binary sensing feature, which detects users' interactions, MagKnitic provides users with tangible cues to interact with physical interfaces in diverse ways.We also provide parametric design templates for users to customize MagKnitic layouts and patterns, which support passive haptic interactions featuring 6 diferent motions.Technical evaluations and user studies validate the efectiveness of our approach.Finally, various application scenarios at diferent scales, from wearable input interfaces like glove-based text input and sleeve-based shape input devices, soft game controllers, to passive haptics systems for VR/AR environments, and large scale objects like interactive furniture coverings, demonstrate the potential of MagKnitic in diferent domains.This research opens up new possibilities for incorporating passive haptic feedback into fabrics, paving the way for the development of innovative and more immersive interactive systems.

Figure 2 :
Figure 2: Principles of MagKnitic.In general, MagKnitic comprises an integrated ferromagnetic patch and a split pocket for permanent magnet placement.Left, As the user moves, bringing the inserted permanent magnet closer to the integrated ferromagnetic yarn, an attractive force is generated and transmitted to the user as a passive force feedback to a specifc interaction.Right, to enable binary sensing, we further integrate commercial conductive yarn into the split pocket.Thanks to the high conductivity of permanent magnet and ferromagnetic yarn, as the user's motion brings the plated conductive pocket with inserted magnet into contact with the integrated ferromagnetic yarn, active electrical paths form and the measured resistance signifcantly drops, enabling binary sensing on the user's interaction accompanied by the passive haptic feedback to the user.

Figure 4 :
Figure 4: Example parametric design template for a MagKnitic design enabling passive haptic feedback during angular interactions.Users were able to defne design-specifc parameters, such as the dimensions of the fipping patch and base structure, as well as the placement of plated ferromagnetic patches, and split pockets.In the middle Knitout visualization, the user-defned parameters are in white.With the user-defned parameters, our pre-programmed design templates output the corresponding .DAT fle on the right using the Knitout compiler, encoding low-level knitting machine instructions and can be imported to the machine for automatic fabrication.

Figure 5 :Figure 6 :
Figure 5: Materials and fabrication.MagKnitic is made of acrylic yarn, ferromagnetic yarn, conductive yarn, and permanent magnets.All specimens are automatically fabricated by an industrial digital knitting machine.

Figure 7 :
Figure 7: Characterization schematics.The customized characterization schematics featuring Left, vertical motion and Right, horizontal motion.

Figure 8 :
Figure 8: Force response of ferromagnetic patches with diferent knitting patterns along vertical displacement towards a fxed permanent magnet.

Figure 9 :
Figure 9: Force response of a ferromagnetic patch (half gauge knit) along vertical displacement towards the fxed permanent magnets with diferent sizes.

Figure 10 :
Figure 10: Force response of linear ferromagnetic knits with diferent arrangements along horizontal displacement towards a fxed permanent magnet.

Figure 11 :Figure 12 :
Figure 11: Force response of a ferromagnetic knit along horizontal displacement towards diferent permanent magnet arrangements.

Figure 13 :
Figure 13: MagKnitic in wristbands.Knitted wristbands with haptic feedback as wearable input interfaces, enabling angular and polar interactions.

Figure 17 :
Figure 17: Furniture covering.Leveraging digital design and fabrication pipeline, MagKnitic can be integrated into furniture coverings, including table cloth, and sofa coverings, for diverse user interactions with passive haptic feedback.Using scenarios include tangible and interactive task checklists, ubiquitous user input interfaces, and so on.

Figure 18 :
Figure 18: User classifcation on force feedback generated by diverse magnet arrangements.The magnet fux layouts generated from diferent magnetic amplitudes and spacing are plotted on the right.

Figure 19 :
Figure 19: Time consumption and input accuracy featuring polar interactions with and without MagKnitic passive haptic feedback.

Figure 21 :
Figure 21: Potential application of passive yet interactive gloves and socks for surface textures rendering in VR environments.