DynaFLIP: Dynamic Flex-and-Flip Manipulation

• DynaFLIP is a dynamic flex-and-flip method that stores and transfers elastic energy to grasp deformable linear objects, such as paper strips.
• It employs a two-phase process where a compliant gripper first flexes the object into an S-shape and then passively flips it into a stable pinch grasp using friction-based contacts.
• Experimental validation in robotic page turning demonstrates high success rates across various paper stiffnesses, highlighting its energy-efficient open-loop operation.

DynaFLIP denotes the dynamic flex-and-flip manipulation process analyzed in “Dynamic Flex-and-Flip Manipulation of Deformable Linear Objects” (Jiang et al., 2023). It is a robotic grasping technique for thin, flexible deformable linear objects lying on a flat surface, including paper strips and pages. The method proceeds in two coupled phases. In the Flex phase, a robotic gripper bends the object into a high-energy configuration while one finger fixes it against the tabletop. In the Flip phase, the stored bending energy drives the object tip to flip into the space between the fingers, where a stable pinch grasp can form. The technique is explicitly developed for open-loop execution and for underactuated, compliant fingers, and is demonstrated in robotic page turning (Jiang et al., 2023).

1. Problem setting and kinematic assumptions

DynaFLIP is formulated for deformable linear objects modeled as elastic, inextensible, thin flexible strips or pages lying initially flat on a rigid, flat surface. The deformation is restricted to a vertical plane containing the object and perpendicular to the tabletop. This planar restriction is central to the modeling: the object is treated as a curve with arc length parameter $s$ and total length $L$, rather than as a fully general three-dimensional deformable body.

The gripper provides two point contacts through a two-finger arrangement. The initial configuration places both fingers on the same side of the object tip, with the distal finger close to the tip so that the distance $\delta$ is small. Finger #1 presses the object to the tabletop and acts as the fixing contact. Finger #2 is lifted off the table and moves to flex the object. The fingers are underactuated, compliant soft fingers driven by pneumatics, specifically fast pneu-net style actuators. Their curvature is approximately linear in pressure, with

$\kappa(P) \approx k_p P,$

where $P$ is internal pressure and $k_p$ is determined by geometry and material.

The finger bases are set at a $90^\circ$ angle. This geometry creates a “pocket” between the fingers, and the pocket is not incidental: it is the receiving region into which the object tip flips during the dynamic phase. A plausible implication is that DynaFLIP is not merely a bending strategy, but a coordinated interaction among object elasticity, compliant actuation, and gripper geometry.

2. Dynamic flex-and-flip mechanism

The core mechanism is an energy-transfer process. During Flex, finger #2 drives the deformable linear object into a bent S-shape while finger #1 holds the object in place. In this phase, kinetic energy of finger #2 is converted into internal bending energy of the object, so that $T_f \downarrow$ while $U \uparrow$. After finger #2 slows to a stop, the contact separates passively. The stored bending energy then propels the tip into the pocket between the fingers, enabling pinch grasp formation as the object passes between them (Jiang et al., 2023).

The object is modeled as an Euler–Bernoulli-like elastic curve with flexural rigidity $R_f = E I$, where $L$0 is Young’s modulus and $L$1 is the second moment of area. With curvature $L$2, the bending energy is

$L$3

Minimum-energy shapes subject to the finger contacts, free slopes at the contacts, distance constraints between fingers, and ground non-penetration produce an S-shape with a single inflection. This S-shape is the mechanically relevant precondition for the subsequent flip.

The transition from Flex to Flip is described through an energy-balance narrative:

$L$4

Here $L$5 denotes gravitational potential, $L$6 is work dissipated by friction and ground interactions, and $L$7 accounts for inelastic effects. In the intended regime, finger kinetic energy is small at the instant the finger stops, and the flip proceeds because stored bending energy decreases along the negative gradient of the energy field.

The paper’s qualitative success conditions follow directly from this mechanism. Sufficient bending energy must be stored; the tip trajectory induced at separation must be directed toward the pocket; the collision between finger and object must be non-perfectly plastic; and there must be relative motion rather than perfect synchrony. Large $L$8 is unfavorable because the tip can become untuckable given the gripper kinematics. This suggests that DynaFLIP depends less on exact trajectory tracking than on entering the correct energetic and geometric regime.

3. Contact mechanics, friction, and failure conditions

The contact model assumes Coulomb friction with friction cones. At each contact,

$L$9

where $\delta$0 is the tangential force magnitude, $\delta$1 is the normal contact force, and $\delta$2 is the coefficient of friction. During Flex, contact #2 must remain within the friction cone; otherwise the manipulation fails through premature slip or loss of contact.

A lower bound $\delta$3 at contact #2 is computed over a grid of finger positions by solving the energy minimization problem and extracting contact forces through Lagrange multipliers. Geometrically, $\delta$4 is obtained from the angle between the object-shape normal at contact #2 and the contact-force direction. The paper does not provide a closed-form expression, but uses a colormap over the configuration space to indicate the required $\delta$5 for quasistatic equilibrium (Jiang et al., 2023). The analysis is quasistatic, so the actual friction requirement during a highly dynamic flip may differ, although the same inequality remains applicable.

Several failure modes are identified. Loss of contact or slip at contact #2 during Flex occurs when the fingertip does not carry the object into high-energy states; the prescribed mitigations are higher fingertip friction, reduced finger speed or ramp rate, and adjustment of $\delta$6 to avoid ground sticking. Insufficient flip occurs when the tip fails to enter the pocket; the prescribed mitigations are reducing $\delta$7 by adjusting $\delta$8, checking that the chosen pressures produce sufficient bending energy, and verifying that the $\delta$9 base angle supplies enough pocket volume. Misalignment and ground sticking occur when $\kappa(P) \approx k_p P,$0 is too small or too large: if $\kappa(P) \approx k_p P,$1 is too small, the fingertip sticks on the tabletop, while if $\kappa(P) \approx k_p P,$2 is too large, the fingertip misses the object entirely.

A common misconception is that such a manipulation must rely on closed-loop force regulation or high-bandwidth sensing. The reported analysis points in a different direction: the decisive factors are friction-cone feasibility, accumulation of elastic energy, and passive contact separation. That does not eliminate the role of sensing, but it shifts the burden of success toward mechanics and configuration selection.

4. Open-loop implementation and compliant hardware realization

The implementation is explicitly open loop. Finger #1 is pressurized to press the object against the table, while finger #2 is pressurized to flex the object and lift off the table, without closed-loop force or motion feedback. In the experiments, the executed pressures are

$\kappa(P) \approx k_p P,$3

AprilTag vision localizes the object, and the arm sets the gripper pose to an initial configuration $\kappa(P) \approx k_p P,$4 before the finger pressures are ramped according to a pre-scripted schedule. Motion playback is identical across trials (Jiang et al., 2023).

Compliance is functional rather than merely tolerable. The soft fingers passively negotiate finger–ground interactions, and compliance enables the “bounce” necessary for contact separation. Finger #2 can store and release energy while interacting with both the object and the ground, then recoil without requiring precise timing control. The finger-tip trajectory is nominally spiral-like as curvature increases; when this trajectory intersects the tabletop constraint, a flat section appears, consistent with non-penetration.

The experimental hardware comprises a UR10 industrial arm, a two-finger soft hand, an RGB palm camera, and SMC electro-pneumatic regulators (ITV 0030-2S). The fingers are fabricated from thermoplastic polyurethane with Ultimaker 2+, their base angle is $\kappa(P) \approx k_p P,$5, and their curvature–pressure relation is measured as approximately linear via OpenCV.

The operational procedure is reported as a six-step routine:

1. Initialization: localize the object tip via AprilTag and move the gripper to initial pose $\kappa(P) \approx k_p P,$6 in the vertical plane perpendicular to the tabletop, with small $\kappa(P) \approx k_p P,$7.
2. Finger placement and fixation: pressurize finger #1 to $\kappa(P) \approx k_p P,$8 MPa to fix the object, and keep finger #2 slightly above the table.
3. Flexing phase: ramp finger #2 to $\kappa(P) \approx k_p P,$9 MPa, producing an S-shaped bend and increasing $P$0.
4. Release/flip phase: allow passive separation; stored bending energy drives the tip into the pocket while the finger recoils downward.
5. Pinch stabilization: form a pinch grasp with the object now between the fingers.
6. Post-grasp handling: execute page turning or another secondary manipulation.

The practical pose-selection guidelines extracted from experiments are

$P$1

and

$P$2

within the tested ranges. Keeping $P$3 as small as feasible is repeatedly emphasized.

5. Experimental validation in robotic page turning

The experimental validation is centered on robotic page turning. The objects include a paper strip in ISO A4 format of $P$4 at $P$5 gsm, whole A4 pages, and papers spanning $P$6–$P$7 gsm. The manipulation is performed in the plane formed by the two fingers and the strip, perpendicular to the tabletop.

The gripper initial pose is parameterized by $P$8 measured from the right tip of the object. The tested ranges are $P$9–$k_p$0 mm in steps of $k_p$1 mm, $k_p$2–$k_p$3 mm in steps of $k_p$4 mm, and $k_p$5–$k_p$6 deg in steps of $k_p$7 deg. At each pose, five repeated trials are performed with $k_p$8 MPa and $k_p$9 MPa. This yields

$90^\circ$0

trials in total. A pose is counted as successful if its success rate is at least $90^\circ$1, equivalently at least $90^\circ$2 successes out of $90^\circ$3 (Jiang et al., 2023).

Successful poses cluster in the $90^\circ$4 space, yielding the experimentally derived relation

$90^\circ$5

If $90^\circ$6 is too large or too small, the feasible ranges for $90^\circ$7 shrink. The $90^\circ$8–$90^\circ$9 relation is well described by an affine least-squares fit.

The multi-material validation uses $T_f \downarrow$0 trials per paper type. The reported success rates are as follows.

Paper type	Success rate
70 gsm	78.5% (51/65)
80 gsm	86.2% (56/65)
100 gsm	89.2% (58/65)
140 gsm	95.4% (62/65)
160 gsm	90.7% (59/65)
200 gsm	93.8% (61/65)

The reported trend is that success rate tends to increase with paper gsm, interpreted in the study as a stiffness effect. The paper further overlays finger-#2 tip paths on a dimensionalized energy field and reports that Flex moves the system toward higher $T_f \downarrow$1, separation occurs near a local maximum where the finger stops, and the object then follows the negative gradient of $T_f \downarrow$2 into the pocket. Large $T_f \downarrow$3 and improper $T_f \downarrow$4 produce failures consistent with friction/contact constraints and pocket-geometry limitations.

6. Comparisons, limitations, and terminological scope

DynaFLIP is compared against several classes of page-turning and grasp-initiation methods. Suction or adhesive methods, including polymer adhesion approaches, can be highly reliable but require specialized end-effectors and surface compatibility. Sweep-and-pinch or quasi-static flip-and-pinch strategies with underactuated rigid fingers may depend more strongly on precise positioning or higher-impedance control to create a gap. DynaFLIP instead uses passive dynamics, elastic energy exchange, compliant actuation, and open-loop execution (Jiang et al., 2023). Nonprehensile dynamic manipulation is an adjacent methodological category, but the reported technique is specialized for thin deformable linear objects and page turning with minimal sensing.

Its limitations are stated directly. Robustness depends on fingertip and surface friction; insufficient $T_f \downarrow$5 at contact #2 can cause slip during Flex. Extremely floppy materials may store insufficient bending energy, while extremely stiff materials may require higher pressures or generate unfavorable contact dynamics. Large $T_f \downarrow$6 degrades flipping because of gripper kinematics and pocket-access constraints. Although open loop is sufficient in the demonstrated regime, very fast dynamics or substantial external disturbances could motivate sensing and feedback. Proposed future improvements include tactile feedback for estimating and controlling frictional forces and extension to deformable $T_f \downarrow$7D planar objects.

The name itself requires care. In deformable-object manipulation, DynaFLIP refers to the dynamic flex-and-flip process associated with page turning and pinch-grasp acquisition (Jiang et al., 2023). The same name is also used by the unrelated paper “DynaFLIP: Rethinking Robotics Perception via Tri-Modal-Dynamics Guided Representation,” which introduces a dynamics-aware multimodal pre-training framework for robot manipulation perception rather than a flex-and-flip grasping method (Lee et al., 28 May 2026). For arXiv readers, this terminological overlap is significant: the two uses share a robotics context, but they address different technical layers, one at the level of contact-rich deformable manipulation and the other at the level of representation learning.