This paper presents analytical closed-form inverse kinematics (IK) solvers for 6R robots with parallel joints via prompting large language models (LLMs). Current IK solvers face a fundamental trade-off: general-purpose algebraic methods become intractable for robots with special architectures, while specialized solvers impose restrictive assumptions such as zero link offsets or fixed twist angles, limiting applicability to real-world robots with arbitrary Denavit-Hartenberg parameters. We develop production-quality analytical solvers tailored to the parallel joint architecture while remaining general across all other kinemaatic parameters using a two-stage LLM-assisted development workflow. In the first stage, we leverage LLM prompting to develop robust helper functions for solving four canonical trigonometric equation systems with degeneracy handling. In the second stage, we inject expert guidance through structured prompts to direct the LLM in deriving and implementing the full IK solver, which strategically decouples the 6R problem into two sub problems: (1) bilinear trigonometric system solving for joints 1 and 6, and (2) planar 3R kinematics for the parallel joints. Validation across 119 real industrial collaborative robots and 100 randomly generated configurations demonstrates 100 10^-9 , confirming suitability for real-time robotic control.

This paper presents a hypothesis-driven artificial-intelligence (AI)-assisted research pipeline for modeling a compliant parallelogram mechanism, using parasitic-rotation prediction as a bounded case study. Domain experts propose and adjudicate physically motivated pseudo-rigid-body model (PRBM) variants, while large-language-model (LLM) coding agents implement models, run finite-element-analysis (FEA) benchmarks, train machine-learning (ML) surrogates, and preserve an auditable hypothesis log. The pipeline tested PRBM variants against a 1547-case FEA-3D dataset and a separate 24-case FEA evaluation set at a fixed normalized half-separation ratio. The examined PRBM extensions could not predict all three outputs across small, medium, and large deflection ranges with one physically interpretable parameterization; the final Gaussian-process (GP) model is therefore presented as a data-driven, geometry-specific surrogate rather than a general analytical reduced-order model. On the evaluation dataset, the GP surrogate gave the best accuracy--speed tradeoff among the evaluated models, winning seven of nine range/output root-mean-square-error cells and predicting in sub microsecond per case, approximately 75 times faster than representative PRBM Newton-solve variants. Code, data, and logs are released for audit.

Abstract This article presents an open-source, hierarchical, eight-level multifidelity modeling stack as a comprehensive technical routine for the design and analysis of compliant mechanisms, utilizing the widely adopted parallelogram flexure as a representative case study. Our methodology involves the systematic implementation, integration, and cross-validation of modeling levels spanning from first-order linear beam theories and refined pseudo-rigid-body models (PRBMs) with optimized characteristic radius factors to intermediate beam constraint models (BCMs), exact transcendental solutions for fixed-guided beams, numerical boundary value problem (BVP) systems, and high-fidelity 3-D solid finite element analysis (FEA). All solvers, benchmarking datasets, and interactive tools have been developed as an open-source contribution to facilitate community adoption and further research. Major results demonstrate an excellent performance spread of over eight orders of magnitude in computational runtime, ranging from submicrosecond algebraic evaluations to solid-mesh simulations requiring nearly a minute per load case. Furthermore, we quantify the localized divergence of low-fidelity models in predicting critical second-order effects, such as parasitic rotations and nonlinear softening/stiffening behavior near-buckling thresholds. Based on the summary of these benchmark test results, a practical model-selection guide is concluded to assist designers in selecting optimal modeling fidelities for various flexure systems, facilitating the rapid synthesis of precision mechanisms with guaranteed accuracy across expansive workspaces.

This paper demonstrates a hypothesis-driven AI-assisted research pipeline for mechanism-design research, using reduced-order modeling of compliant parallelogram flexures as a bounded but unresolved case study. The central question is methodological: can a domain expert and AI agents move from physical hypotheses to falsification, model revision, benchmarking, visualization, and manuscript-ready evidence without losing scientific traceability? Human judgment is reserved for problem framing, physical hypothesis generation, falsification decisions, and final claim adjudication, while AI agents implement models, run finite-element and optimization sweeps, build comparison tools, train surrogate models, and maintain the evolution log. The pipeline systematically tested plausible PRBM extensions against FEA-3D parasitic-rotation data, identified why they did not resolve the rotation-error problem, and converged on a differentiable Gaussian-process surrogate with the strongest accuracy--efficiency tradeoff among the evaluated models. We do not claim that this ML model is the ultimate reduced-order solution. Instead, it is sub-millisecond, much faster than PRBM Newton-solve variants, and more accurate than BCM across medium and large deflections. Code, data, the comparison app, and the hypothesis log are released.

This paper presents a large language model (LLM) assisted process for developing analytical closed-form inverse kinematics (IK) solvers for robot manipulators. The collaborative workflow enables human experts supervise AI agents through carefully designed prompts, while AI handles all coding, symbolic manipulation, and testing. This division of labor leverages each party’s strengths: human intuition for problem decomposition and strategic guidance versus AI capability for systematic execution of labor-intensive tasks. The methodology comprises two key components: (1) a library of robust helper functions for common trigonometric equation systems, and (2) structured prompts that direct AI agents through derivation, code generation, and validation. Refined prompts significantly reduce iterative exchanges. We demonstrate the methodology on two major 6R robot architectures—spherical wrists and parallel joints—representing over 90% of industrial manipulators. The resulting solvers achieve 100% success rates across 842 industrial robots and 1000 random configurations, with working code produced in minutes rather than weeks. This work establishes a new paradigm where human expertise guides AI execution, significantly reducing development time while maintaining mathematical rigor.

Abstract Designing soft robots is challenging due to their infinite degrees of freedom and high flexibility, which limits their payload capacity. This paper presents a systematic framework for designing and analyzing compliant mechanisms driven by PneuNets bending actuators. The stiffness ratio of the compliant mechanism allows soft robots to carry higher payloads. We design two compliant joints–revolute and prismatic–and verify them through finite element simulations and physical prototypes. A kinetostatic model for the single joint, based on machine learning and the Pseudo-rigid-body model, is developed and integrated into the robotic system. A 3R planar robotic arm is used to evaluate the design and analysis models. The results show that the error of the kinetostatic model is below 5%, and the robotic arm can continuously control target positions with an error of less than 0.5.

This paper presents analytical solvers for four common types of algebraic equations encountered in robot kinematics: single trigonometric equations, single-angle trigonometric systems, two-angle trigonometric systems, and bilinear two-angle systems. These equations arise frequently in the kinematics problems, particularly in robot kinematics. We provide detailed solution methods, including closed-form expressions, numerical algorithms, and robustness considerations. The solvers are designed to handle general coefficients, manage singularities, and enumerate all real solutions efficiently. These solvers are implemented in Python packages and can be reproduced by prompting Language Lanuage Models. Sampe prompts are also provided in the public code space Github repo. These prompts can generate a working solver code with one single prompt in coding agent such as OpenAI's Codex 5.1. This work serves as a foundation for developing complete inverse kinematics solvers for various robot architectures. Extensive validation and benchmarking demonstrate the effectiveness and reliability of the proposed methods.

While soft robots enjoy the benefits of high adaptability and safety, their inherent flexibility makes them suffer from lower load-carrying capacity and low motion precision, which limits their applications to a broader range of fields. In this paper, we propose an active hinge joint with a hard backbone combined with soft pneumatic actuators to overcome this challenge. We detail the design, theoretical modeling, and experimental testing of a novel compliant hinge joint driven by two pneumatic networks (PneuNets) bending actuators. The joint is constructed by attaching the two actuators to a cross-spring pivot’s two flexible leaf springs. Pressurizing one of the actuators can drive the joint to rotate clockwise or counterclockwise about the central axis. A Pseudo-rigid-body model is developed to analyze the kinematics and statics of the joint. FEA simulation and experimental experiments have been developed to validate the model. The results show that the joint can achieve ± 43° under 0.276 MPa, and the pressure-displacement curve is close to linear. Experiments are also conducted to measure the joint’s in-axis and the other three off-axis stiffness. After calculating the stiffness ratio, the results show that the three off-axis stiffness (Kθx, KY, KZ) are 16.74, 471.75, and 627.63 times the in-axis stiffness (Kθz), respectively. It means our hinge joint can carry a high payload off-axis while maintaining the in-axis flexibility.

Soft pneumatic linear actuators are crucial elements in soft robots. Although those highly flexible and extensible actuators accelerate the development of soft robots, their inherent softness leads to significant disadvantages such as low load-carrying capacity and large motion error limit. In this paper, we propose a new class of soft pneumatic linear actuators with a compliant parallelogram mechanism as a backbone combined with Pneumatic network (PneuNets) bending actuators. The new actuator has flexibility in the motion direction while maintaining a higher stiffness in other directions. We derive the actuator's pressure-displacement model by the Pseudo-rigid-body model and validate it by experiments and simulations. The stiffness measurement results show that the off-axis stiffness in the Y and Z directions are 188.327 and 5.469 times the in-axis stiffness, respectively. The proposed soft linear actuator design offers an alternative solution for enhancing the performance of soft robots.

Layer jamming (LJ) materials and structures have shown promise in designing variable stiffness compliant mechanisms for robotics. However, design challenges persist due to time-consuming prototyping, testing, and significant compu-tational resources needed for finite element (FE) simulations. The complexity stems from the intricate mechanics behavior between jamming materials and substrate structures. This article presents a hybrid model that combines machine learning (ML) with data generated from finite element (FE) analysis to predict the mechanical behavior of LJ -based compliant parallel-guided mechanisms, including force-deflection relationships, stiffness, and hysteresis. An experimentally validated FE model generates data by varying geometric and material parameters, capturing key mechanical performance metrics. This data serves as input for training a neural network model, which evaluates the impact of selected design parameters on performance metrics. The resulting ML model is highly efficient, with predictions taking seconds compared to hundreds of hours needed for FE simulations, and remarkably accurate, with less than a 5% error relative to FE simulations. This efficient computational model can be used for designing and analyzing LJ-based parallel-guided mechanisms, with the validated workflow process applicable to other LJ -compliant mechanisms and robotic systems.

This article presents a novel soft robotic gripper with a high payload capacity based on the layer jamming technology. Soft robots have a high adaptability, however suffer a low payload capacity. To overcome these conflicting challenges, here we introduce a 3D printed multi-material gripper that integrates jamming layers for enhancing payload capacity. By inflating the internal air chamber with positive pressure, the finger can be actuated to a large bending angle for adapting complex shapes. Layers of jamming sheets are bounded on the finger structure and are then sealed inside a vacuum bag. When a high payload is desired, air inside the vacuum bag is drawn out and a negative air pressure is applied to the jamming layers, which leads to the gripper locked at the actuated shape. To evaluate the performance of the gripper, we conducted extensive tests including actuation, stiffness variation, typical payload capacity, and adaptability. The results show that our gripper is not only highly adaptable just like most soft grippers but also more importantly capable of grasping heavy (about 6-10 kg) objects comparable to rigid-body counterparts.

Structural DNA nanotechnology has enabled the design and construction of complex nanoscale structures with precise geometry and programmable dynamic and mechanical properties. Recent efforts have led to major advances in the capacity to actuate shape changes of DNA origami devices and incorporate DNA origami into larger assemblies, which open the prospect of using DNA to design shape-morphing assemblies as components of micro-scale reconfigurable or sensing materials. Indeed, a few studies have constructed higher order assemblies with reconfigurable devices; however, these demonstrations have utilized structures with relatively simple motion, primarily hinges that open and close. To advance the shape changing capabilities of DNA origami assemblies, we developed a multi-component DNA origami 6-bar mechanism that can be reconfigured into various shapes and can be incorporated into larger assemblies while maintaining capabilities for a variety of shape transformations. We demonstrate the folding of the 6-bar mechanism into four different shapes and demonstrate multiple transitions between these shapes. We also studied the shape preferences of the 6-bar mechanism in competitive folding reactions to gain insight into the relative free energies of the shapes. Furthermore, we polymerized the 6-bar mechanism into tubes with various cross-sections, defined by the shape of the individual mechanism, and we demonstrate the ability to change the shape of the tube cross-section. This expansion of current single-device reconfiguration to higher order scales provides a foundation for nano to micron scale DNA nanotechnology applications such as biosensing or materials with tunable properties.

软体机械手在易损物品抓取方面具有其独特的优势,近年来成为机器人领域的研究热点.为便于评价软体机械手的整体性能,实现其精确抓取控制,需要对软体机械手进行建模分析与试验研究.本文设计了四指软体机械手,每个手指单元内置用于实时检测机械手弯曲角的柔性应变传感器;建立了不同气压作用下的弯曲角和末端输出力特性的数学模型,并分析限制层刚度变化对软体手指输出特性的影响;设计了软体机械手控制系统,在此基础上开展软体手指的弯曲角和末端输出力特性试验,试验结果表明调节限制层刚度可有效改善输出力,理论分析与试验结果吻合,验证了数学模型的正确性.对几种不同质量的常用水果(如草莓、橘子、梨、苹果)的抓取试验结果表明,软体机械手能够实现对易损物体的无损抓取,其包络抓取力最大为11.89 N,指尖抓取力最大为2.81 N.

ABS T R A C T In recent years, soft pneumatic actuators with soft and flexible materials have been widely studied in the field of soft gripper and soft bionic robot. Up to present, the soft actuators studied usually have one motion manner such as extending, bending, twisting or rotation. In this paper, we propose a new type of multi-degree-of-freedom soft pneumatic actuator (MDoF SPA) that can extend or rotate in response to pressured air inputted in different chambers. A fabrication method was proposed. A mathematical model based on large deformation theory was presented to predict the elongation displacement and bending angle. Moreover, finite element analysis and experimental investigation were performed to verify the theoretical results. The output force during elongation and blocking force during bending were also tested. Finally, two MDoF SPAs were utilized to fabricate a crawling robot. The gait and hardware of crawling robot were shown. The average moving speed of linear motion, maximum bending angle were investigated as well. Experiments revealed the robot actuated by MDoF SPAs has a good comprehensive performance, which has great potential in search, detection, rescue and other operations in a narrow environment. This work can guide the design and application of MDoF SPAs in the future.

With the superior ductility and flexibility brought by compliant bodies, soft manipulators provide a nondestructive manner to grasp delicate objects, which has been developing gradually as a rising focus of soft robots. However, the unexpected phenomenon caused by environmental effects, leading to high internal nonlinearity and unpredictable deformation, makes it challenging to design, model, and control soft manipulators. In this paper, we designed a soft pneumatically actuated manipulator consisting of four soft actuators, as well as a flange, and investigated the influence of structural parameters on the output characteristics of the manipulator through finite element analysis (FEA). To enhance the bending deformation of the soft actuator, annular rings were employed on the soft actuator. A mathematical model for the bending deformation of air cavities was established to explore the relationship between the driving pressure and the bending angle based on the Yeoh strain energy function. Moreover, an end-output force model was established to depict the variation of the force output with the bending angle of the soft actuator, which was then experimentally validated by adopting the manufactured manipulator. The soft actuator studied in this paper can bend from 0° to 110° under an applied pressure of 0–60 kPa, and the maximum grasping load of the soft manipulator is 5.8 N. Finally, practical tests were conducted to assess the adaptability of the soft manipulator when grasping delicate fruits, such as apples, pears, tomatoes, and mangoes, demonstrating its broad application prospects in nondestructive fruit harvesting.

Flexible sensing tends to be widely exploited in the process of human–computer interactions of intelligent robots for its contact compliance and environmental adaptability. A novel flexible capacitive tactile sensor was proposed for multi-directional force sensing, which is based on carbon black/polydimethylsiloxane (PDMS) composite dielectric layer and upper and lower electrodes of carbon nanotubes/polydimethylsiloxane (CNTs/PDMS) composite layer. By changing the ratio of carbon black, the resolution of carbon black/PDMS composite layer increases at 4 wt%, and then decreases, which was explained according to the percolation theory of the conductive particles in the polymer matrix. Mathematical model of force and capacitance variance was established, which can be used to predict the value of the applied force. Then, the prototype with carbon black/PDMS composite dielectric layer was fabricated and characterized. SEM observation was conducted and a ratio was introduced in the composites material design. It was concluded that the resolution of carbon sensor can reach 0.1 N within 50 N in normal direction and 0.2 N in 0–10 N in tangential direction with good stability. Finally, the multi-directional force results were obtained. Compared with the individual directional force results, the output capacitance value of multi-directional force was lower, which indicated the amplitude decrease in capacity change in the normal and tangential direction. This might be caused by the deformation distribution in the normal and tangential direction under multi-directional force.

In this research, a soft robotic gripper with a variable stiffness enabled by a novel positive pressure layer jamming technology was developed and fabricated in two materials using customized additive manufacturing. A novel positive layer jamming technology was developed for tuning stiffness of the gripper. Positive pressure layer jamming has a higher performance potential than conventional vacuum layer jamming since a higher pressure can be applied, approximately 1.6x higher in terms of payload capacity. Two different thermoplastics materials are printed together to form a relatively hard backbone and a relatively soft airtight actuation bellows. The implementation of positive layer jamming will be described, along with the additive manufacturing techniques used to produce the gripper and the test results of the final design. Experimental tests show that this soft gripper was able to vary its stiffness about 25x fold with the positive layer jamming. This work demonstrates that the positive pressure jamming offers a novel method for varying soft robot stiffness with higher payload capacity than the conventional vacuum based layer jamming technology.

In this paper, we introduce the key elements of a computational tool and a comprehensive methodology for enabling simulation-informed design of robotic ankle prostheses. Our approach is based on trajectory optimization methods for predicting human walking gait applied to a model of a bilateral lower leg amputee with robotic ankle prostheses. The goal of this simulation tool and design methodology is to provide a means to evaluate the performance of a prosthetic design and its effect on adapting human walking gait before involving human subject studies. The gait prediction problem is formulated as a multi-objective trajectory optimization of a multibody dynamic system within the existing framework of the open-source biomechanics package, OpenSim. Our approach models the effects of a planar human model with legs and torso, Hill-type muscle actuators, a closed-loop linkage for the robotic prosthetic device, and a DC motor dynamics model. To demonstrate the gait prediction process in use for design evaluation, we include a pair of example design evaluation simulations. In the first example, the gait prediction method shows that the initially proposed prosthesis design fails to improve the human effort estimated by cubic muscle excitations. In the second example, after the selection of a different actuator, the gait prediction method shows that the modified design has the potential to relieve some of the effort of walking required from the amputee. These examples combine to demonstrate how our methodology may be useful for design.