Angle-programmed tendril-like trajectories enable a multifunctional gripper with ultra-delicacy, ultrastrength, and ultraprecision

Soft robotic grippers are sought for applications ranging from biomedicine and minimally invasive surgery to deep-sea exploration, agriculture, food processing, and prosthetics. However, a central challenge is the tradeoff between delicacy, strength, and precision: softness aids safe, adaptive grasping but often sacrifices payload capacity and precise manipulation, while designs that increase strength can compromise gentle, noninvasive interaction and precision, especially with ultrathin or tiny objects. Prior solutions (e.g., suction, variable stiffness, stimuli-responsive materials, and kirigami/origami structures) have improved individual aspects but not unified ultradelicacy, ultrastrength, and ultraprecision in a single device. This study addresses whether explicitly programmed, tendril-like grasping trajectories—implemented via an angle-based kirigami design—can overcome this tradeoff to enable a single gripper to handle ultrasoft liquids, ultrathin sheets/fibers, and ultraheavy loads, while being lightweight, scalable, and integrable with robotic arms and prostheses.

Existing soft grippers employ fluid-driven actuators, compliant elastomers, origami/kirigami, and stimuli-responsive materials, enabling pinching, enveloping, suction, and entangling grasps with adaptive softness. DEA-based and hydraulic grippers can delicately handle fragile items (e.g., raw eggs, jellyfish) but exhibit low payload-to-weight ratios (≈1–80). Variable stiffness approaches (e.g., shape memory polymer grippers) achieve high payloads (ratio up to 6400) but often lose delicacy and noninvasiveness; suction and jamming can damage gelatinous organisms. Precision grasp of tiny or ultrathin objects remains difficult; solutions like extended appendages (kirigami shells) can pinch small grains, and electroadhesion can handle thin sheets but requires smooth, dry surfaces. Prior kirigami-based grippers demonstrated adaptive morphologies and some universality, yet explicit programming and control of grasping trajectories have been underexplored due to nonlinear deformations and implicit relationships between actuation and shape. Biological inspirations (tendrils, tentacles) suggest leveraging nastic trajectories for performance gains, but translating these trajectories into explicitly controlled soft grippers has been limited.

Design: A thin sheet patterned with parallel cuts forms a central X-shaped ribbon network with an original intersecting angle γ0 (or ψ0). Uniaxial stretching increases the intersecting angle toward 180°, causing ribbons to buckle into a pop-up, two-petal shell bridged by cones, producing tendril-like trajectories. PET sheets (thickness 127 µm) were laser-cut (Epilog 40 W) with representative ribbon width 1.5 mm. The design enables explicit control of trajectory via an analytical relationship between applied strain ε and intersecting angle (ε = cs(sin(ψ/2)/sin(ψ0/2) − 1)). Analytical modeling: Discrete ribbons are approximated as Euler elastica; Cartesian trajectory coordinates are derived using elliptic functions with elliptic modulus and rotation angle dependent on γ0 and ε. Key relationships include curvature varying approximately linearly with strain (κ ∝ ε) and maximum trajectory curvature scaling with the square root of angle variation (κmax ∝ √(180° − γ0)). The grasping/closing angle α between end effectors at full deployment is predicted via an expression involving elliptic moduli of spherical/conical ribbon regions, correlating with γ0. Finite element analysis (Abaqus/Standard): PET modeled as isotropic linear elastic (E = 3.5 GPa, ν = 0.38), meshed with C3D10H elements; right end fixed, prescribed displacement on left; fine mesh near ribbon connections. Mechanical testing: Uniaxial tensile tests on Instron 5944 (loading rate 10 mm/min) to obtain force–displacement (Fx–dx) curves for grippers with different γ0. Touch force Fy (reaction in y between petal and object) measured during approach; pulling-out force Fz measured by extracting encapsulated spheres (different diameters) from fully deployed grippers to simulate heavy-object slip scenarios and characterize bending-to-stretching transitions in the geodesic ribbon network. Demonstrations: Integration with a robotic gripper (Robotiq 2F-85 on UR5e) via a 3D-printed adapter (VeroWhite, Stratasys Objet 260) for grasping heavy objects and delicate targets, including water droplets on hydrophobic surfaces, 2 µm fibers, and 4 µm sheets (Toray Lumirror F56). Biodegradability tested by fabricating grippers from natural leaves (e.g., dracaena) for noninvasive grasping (dandelion, food items). Prosthesis integration: Kirigami gripper mounted on an EMG-controlled electrical terminal device (ETD). Surface EMG collected from ECRL and FCR muscles (MA400 system, 1000 Hz sampling) to drive ETD motion; wrist flexion/extension mapped to gripper close/open. Tasks included picking grapes, opening a circular zipper, turning a page, and folding garments.

• Programmable tendril-like trajectories: Analytical and experimental results show trajectory curvature increases approximately linearly with strain (κ ∝ ε), and maximum curvature increases with decreasing γ0 following κmax ∝ √(180° − γ0). Smaller γ0 yields curlier, tendril-like paths; γ0 ≈ 80° produces a near-spherical enclosure (α ≈ 180°) ideal for noninvasive encapsulation.
• Ultragently low contact pressure: Touch force Fy remains small; measured contact pressure ≈ 0.0468 kPa, comparable to state-of-the-art gentlest grippers handling jellyfish (~0.0455 kPa).
• Ultrastrength via bending-to-stretching transition: In fully deployed state, pulling-out force Fz exhibits a dramatic increase due to straightening of the geodesic ribbon network. For γ0 = 80°, as dx increases from 32.5 mm to 40 mm, Fz jumps from ~0.41 N to ~16.3 N (≈39×). Grippers with γ0 = 130° or 150° have maximum Fz < 0.3 N. At full deployment, Fz can exceed Fy by >460×.
• Record payload-to-weight ratio: A 0.4 g gripper lifted a 6.4 kg deadweight (ratio 16,000), surpassing prior reported record of 6400 by 2.5× and exceeding previous curvature-based kirigami designs by 16×.
• Ultraprecision on ultrathin targets: Successful grasping of a 4 µm-thick polymer sheet and a 2 µm-diameter fiber (20× and 40× thinner than a typical human hair, respectively) on flat surfaces, enabled by the curled trajectory and near-180° closing angle that gently scoops with minimal lateral disturbance.
• Universality across materials and forms: Noninvasive handling of liquids (water droplets, bubbles, ketchup, raw egg yolk), soft gels (pudding, caviar), live gelatinous organisms (jellyfish, fish), granular/rigid items (pills, coins, ice cubes), sharp medical waste (needles, sharps), and slippery/fragile foods (strawberry, meat).
• Integration and performance: Lightweight, displacement-controlled actuation simplifies integration with robotic arms and prostheses. Demonstrated tasks include picking grapes noninvasively (success rate ~78.6%), opening a circular zipper, turning a page, and folding garments. Overall grasping success rate reported at ~95.2% without damaging targets.
• Biodegradable implementation: Functional grippers fabricated from natural leaves enable eco-friendly, noninvasive manipulation (e.g., dandelion).

By explicitly programming and controlling grasping trajectories through the kirigami X-shaped angle γ0, the gripper emulates plant tendrils’ nastic, gradually curling motion, directly addressing the delicacy–strength–precision tradeoff. The tendril-like trajectory and near-spherical enclosure enable nondestructive, ultragentle contact while the structure’s energy landscape transitions from bending to stretching under load, providing exceptional holding force and payload capacity. Analytical models accurately predict trajectory shape, curvature–strain relationships, and final grasping angle, facilitating displacement-based control suitable for robotic arms and prostheses without complex feedback. This unification of ultradelicacy, ultrastrength, ultraprecision, universality, and multifunctionality surpasses prior designs that emphasized adaptivity but lacked trajectory programmability. The material- and scale-independent approach, including biodegradable versions, broadens applicability to sensitive biological tasks, food handling, minimally invasive medical tasks, and field robotics (e.g., marine biology).

This work introduces an angle-programmed kirigami gripper whose tendril-like trajectories are both programmable (via γ0) and explicitly controllable (via strain/displacement), enabling ultragentle, ultrastrong, and ultraprecise grasping in one device. It achieves record payload-to-weight performance (16,000), minimal contact pressure (~0.0468 kPa), and precise handling of ultrathin fibers and sheets, while integrating seamlessly with robotic arms and EMG-controlled prostheses to perform delicate, real-world tasks. The analytical framework links geometry to trajectory and grasping angle, guiding design for target tasks. Future directions include optimizing materials (higher modulus and toughness) to improve durability and strength with consideration of energy input; refining boundary geometry to maintain smooth, continuous surfaces; tailoring cut width and aspect ratios; and scaling to different sizes to match target dimensions for consistent enclosure and holding force. The eco-friendly, biodegradable implementations suggest further exploration of sustainable soft robotic systems.

• Target size constraints: If the object is too large to be fully encapsulated, petals may pinch rather than enclose, causing a sharp reduction in holding force (e.g., pulling-out force can drop from ~15 N to ~0.5 N).
• Material tradeoffs: Using stiffer, tougher materials can enhance durability and payload but requires higher input energy/force during stretching.
• Surface smoothness/continuity: Maintaining C2 continuity of upper/lower boundaries is important for smooth curved surfaces; discontinuities can degrade performance on extremely soft targets unless localized ribbon geometry is adjusted.
• Durability considerations: Although maximum principal strains are small and >1,000 cycles of 1 kg lifting were achieved, long-term durability depends on mitigating stress concentrations (e.g., rounding cut tips) and material selection.
• Geometric parameters: Performance depends on optimized ribbon aspect ratios and cut widths; suboptimal parameters or improper γ0 selection can reduce delicacy or strength.