Cylindrical Tangible Proxy in VR/MR

• Cylindrical tangible proxy is a hand-held device with a right-cylindrical design that enables precise, low-fatigue manipulation in VR/MR environments.
• It integrates embedded 6-DoF tracking and shape-changing components to support accurate 4-DoF tabletop interactions and haptic retargeting.
• Empirical studies show that these proxies significantly improve precision and efficiency over hand-based methods in multi-DoF tasks.

A cylindrical tangible proxy is a physical, hand-held device with a right-cylindrical geometry engineered to serve as a direct, embodied controller for virtual or mixed-reality (VR/MR) systems. Such proxies leverage the affordances of cylindrical form—especially their natural support of planar translation, axial rotation, and uniform scaling—to enable precise, low-fatigue manipulation of virtual objects with direct physical feedback. Recent research has established the cylindrical tangible proxy as a high-precision interface for 4-degree-of-freedom (DoF) table-top object manipulation in MR, and as the core element in shape-shifting haptic retargeting devices for VR.

1. Physical Form and Mechanical Design

Cylindrical tangible proxies share several defining characteristics:

• Geometry: Typically a right circular cylinder with a flat base; representative dimensions are an 110 mm diameter and 47 mm height, with a total mass of ~270 g, as implemented in 3D-printed PLA with internal instrument cavities (Mosquera et al., 15 Nov 2025).
• Affordances: The lateral curved surface enables precise 1 DoF rotation around the vertical axis (knob-like manipulation). The flat bottom ensures stable 2 DoF planar translation across a horizontal surface, with the device’s weight further contributing to haptic realism and minimizing inadvertent movement.
• Component Integration: Cylindrical proxies can house standard 6-DoF tracked controllers (e.g., Magic Leap 2), providing robust tracking signals and facilitating integration into commercial MR frameworks (Mosquera et al., 15 Nov 2025).
• Custom Mechanical Variants: Advanced shape-changing proxies, such as Adaptic, comprise four linked, foam-clad, flattened-cylindrical segments connected with double-hinged joints actuated by Mg90S micro-servos. This provides 4 DoF of programmable curvature for morphing between prismatic and cylindrical forms (Gonzalez et al., 2024).

2. Sensing, Tracking, and Control Pipeline

The critical functionality of a cylindrical tangible proxy is its accurate, low-latency mapping between physical motion and virtual object transformations.

• Embedded Tracking: Vision-based and IMU-based 6-DoF controllers are embedded within the proxy, with pose updates sampled at 60–120 Hz or every 100 ms (Mosquera et al., 15 Nov 2025).
• Interaction State Initialization: At the onset of manipulation (triggered by pressing an interaction button), the system snapshots the proxy’s pose $(\mathbf{p}_0, \varphi_0)$ and reports subsequent position and yaw changes as $\Delta x = x(t) - x_0$, $\Delta y = y(t) - y_0$, and $\Delta \varphi = \varphi(t) - \varphi_0$.
• Direct Mapping: The proxy’s 2D displacement maps 1:1 to virtual object translation, yaw rotation maps to object yaw, and, in “scale” mode, rotational displacement maps to uniform scale adjustment, with sensitivity $k$ configured to match desired control granularity (Mosquera et al., 15 Nov 2025).

Shape-changing proxies integrate additional control layers:

• Actuation Feedback: Hinged segments report joint angles via potentiometers; servos are controlled via a microcontroller (e.g., Teensy 3.5), updating positions at 50–100 Hz (Gonzalez et al., 2024).
• Shape Trajectory Generation: Target joint angles for shape morphing are computed offline by minimizing $\sum_n \|P_n(\theta)-V_n\|^2$, where $P_n$ are surface points of the proxy, and $V_n$ are corresponding points on the intended virtual surface.
• Haptic Retargeting: The pose of the real proxy and the user’s hand are mapped to virtual counterparts with an offset $\Delta \mathbf{X}$, using body-warp techniques and incremental gain warping within human steerable-gain detection thresholds (Gonzalez et al., 2024).

3. Interaction Techniques and Transform Mappings

The cylindrical tangible proxy supports multiple interaction modes, configured for task-adaptive DoF:

Mode 1: Translate + Rotate (3 DoF)

• Virtual object position: $$\mathbf{t}_\mathrm{obj}(t) = \mathbf{t}_\mathrm{obj}(t_0) + [\Delta x, \Delta y, 0]^T$$
• Virtual object yaw: $$\theta_\mathrm{obj}(t) = \theta_\mathrm{obj}(t_0) + \Delta\varphi$$

Mode 2: Scale (1 DoF)

• Uniform object scale: $$s_\mathrm{obj}(t) = s_\mathrm{obj}(t_0) + k\Delta\varphi$$

These couplings leverage the proxy’s constrained movement: tabletop support eliminates vertical and roll drift, while the curved surface affords natural, decoupled yaw rotation input (Mosquera et al., 15 Nov 2025). In shape-morphing devices, segmental curvature approximates a virtual cylinder’s radius $R$ by computing per-hinge angles $\theta_i = f_i(R, \text{segment } i)$ (Gonzalez et al., 2024).

4. Performance Metrics and Experimental Findings

Empirical studies consistently demonstrate superiority of cylindrical tangible proxies over hand-midair interaction for multi-DoF tasks. Key results (Mosquera et al., 15 Nov 2025):

Task	Completion Time (TAN, s)	Completion Time (Hand, s)	Effect Size
Only-Move	3.31 ± 1.42	9.78 ± 3.11	large (r=1.00)
Move-And-Rotate	5.47 ± 2.26	11.85 ± 4.18	large (r=1.00)
Combined 4 DoF	12.42 ± 5.08	17.72 ± 7.91	large (r=0.73)

Tabletop use of a cylindrical proxy yielded position errors as low as 1.95 mm and rotation errors below 0.56°, with statistically significant improvements in precision and reductions in corrective overshoot episodes compared to hand-based interaction. For isolated scaling or rotation, improvements were moderate, attributable to added modal switching demands (Mosquera et al., 15 Nov 2025).

In haptic retargeting contexts, Adaptic’s proxy enabled completion times and accuracy metrics equivalent to those of dedicated shape-matching props, with only a modest (~35%) delay under conditions requiring substantial spatial retarget gains. Subjective realism was high: 86% of participants preferred matching shape proxies, and 83% were unaware of spatial incoherence introduced by retargeting (Gonzalez et al., 2024).

5. Design Principles, Affordances, and Interaction Constraints

Recent research distills several design guidelines for cylindrical tangible proxies:

• Physical Stability: Use a flat-bottomed cylinder to constrain DoF and leverage tabletop stability for lower fatigue and higher input precision (Mosquera et al., 15 Nov 2025).
• Ergonomics: Moderate diameter (~11 cm) and weight (~270 g) optimize grasp comfort and minimize inadvertent movement while keeping the device manageable for frequent repositioning.
• Low-Friction Base: A soft cloth or PTFE pad on the bottom facilitates smooth, error-free translation.
• Button Placement: Dedicated “interaction” and “mode” buttons, positioned for full-range access, support functional engagement/disengagement and rapid mode switching during compound tasks.
• Robust Tracking: Embedding a commercial 6-DoF controller enables out-of-the-box tracking with minimal calibration.
• Interaction Mapping: One-to-one mappings of physical motion to virtual transformations are preferred, supporting transparency and user predictability.

For dynamic proxies, it is recommended to employ modular segmentation, shaping and latching mechanisms (locking shapes passively after transformation), and to consider hybrid actuation (combining passive structure with embedded active cues such as vibrotactile feedback) (Gonzalez et al., 2024).

6. Limitations, Trade-Offs, and Future Directions

Cylindrical tangible proxies are subject to inherent and implementation-specific constraints:

• Degree-of-Freedom Reduction: Limiting the proxy to 4-DoF manipulation (planar translation, yaw, scaling) increases precision and reduces fatigue but restricts interaction space compared to unconstrained 6-DoF movement. This trade-off is advantageous for tabletop MR scenarios but less suited for freehand spatial interaction (Mosquera et al., 15 Nov 2025).
• Modal Overhead: Use of “mode” buttons to switch between rotation and scaling introduces cognitive load, increasing completion time in compound tasks. Future designs may benefit from dual-coupled gesture mappings or always-on controls.
• Shape-Changing Fidelity: Hinge-segment proxies (e.g., Adaptic) are limited by the number and range of joints, acting as polygonal approximations to ideal cylinders. Achieving finer curvature requires more, smaller segments or alternative actuation such as SMA or pneumatic mechanisms (Gonzalez et al., 2024).
• Torque and Force Output: The practical force exerted by micro-servos for morphing proxies is limited (2.5 kg·cm per servo). Handling heavier or higher-load scenarios may necessitate upscaled, geared, or pneumatic actuators.
• Update Rate: Shape transition times of ~3 s are acceptable for per-grasp or between-object adjustments but insufficient for fast, continuous deformation. This may constrain applicability in highly dynamic VR scenarios (Gonzalez et al., 2024).

A plausible implication is that, as actuators, tracking, and haptic retargeting algorithms continue to develop, cylindrical proxies—especially modular, shape-adaptive variants—will be integral to scalable, multi-object physicalization for high-precision VR and MR interaction.

7. Related Systems and Theoretical Context

The TanGi toolkit provides a generalizable architecture for composable physical proxies in VR, but notably, its primitives do not include cylinders, offering only cubic, triangular, half-spherical, and rod-like (unparameterized) elements (Feick et al., 2020). Thus, research-driven implementation of cylindrical proxies requires bespoke mechanical design and sensor embedding. In contrast, studies of hand interaction versus tangible proxies show that cylindrical designs yield measurable benefits in manipulation tasks—especially in compound, multi-DoF scenarios.

Finally, the development of haptic retargeting frameworks, as exemplified by Adaptic, demonstrates that cylindrical proxies with programmable geometry can stand in for a broad repertoire of virtual objects, provided that haptic warping and physical-to-virtual mapping strategies remain within perceptual tolerances. This position is supported by recent empirical findings indicating minimal awareness of spatial incoherence and strong user subjective preference for tactilely congruent, shape-matching proxies (Gonzalez et al., 2024, Mosquera et al., 15 Nov 2025).