Kinematic Chain

Overconstrained rational single-loop linkages are efficient, compact, and low-cost custom mechanisms, yet their deployment in industrial settings is limited. In simulations, rigid body formulations fail due to redundant constraints. This study presents a flexible multibody modeling framework based on the floating frame of reference formulation, and delivers an overall accuracy analysis of assembled linkages prototypes. The approach is validated against 3D-printed PLA prototypes of a Bennett four-bar mechanism, including variants with intentional joint-axis misalignment, which theoretically, from the rigid body point of view, cannot be assembled. A supplementary contribution is delivered in the form of a kinematic parameter identification methodology suited for this type of mechanism with ill-conditioned Jacobian. The experimental and simulation results are compared and reveal that these overconstrained mechanisms exhibit a self-assembling tendency -- structural compliance drives the assembly toward the ideal geometric configuration, distributing constraint stress throughout the structure. Additional qualitative demonstrations using cardboard tubes and bamboo sticks as link building blocks confirm that functional mechanisms can be realized from low-cost, unconventional materials with limited manufacturing accuracy. The proposed modeling pipeline is fully algorithmic and enables design optimization in the future.

This paper presents a low-clearance hinge joint mechanism based on the 3D printing on sheet fabrication method. This approach simplifies the fabrication of hinge mechanisms and overcomes limitations of conventional origami manufacturing by eliminating the need for adhesives commonly used during assembly, making it suitable for robots at the tens-of-centimeters scale. The advantages and disadvantages of three types of hinge joint mechanisms are compared, and a hinge joint that can be designed with low clearance for various facet thicknesses is selected. Based on the selected hinge joint, the twisting angle and bending force are analyzed, leading to the implementation of a clearance of 0.1 mm. Torsional resistance is experimentally evaluated to measure the torque required for twisting caused by plastic deformation and clearance. The results show that the torque associated with plastic deformation is sufficient to constrain the undesired degrees of freedom of the hinge joint, while the torque required for twisting due to clearance is minimal. Based on the analyzed data, the proposed hinge joint mechanism is applied to a 3-degree-of-freedom delta robot manipulator, demonstrating precise motion with low clearance.

Closed kinematic chains complicate modular modeling by coupling active and passive coordinates through nonlinear closure constraints. This paper presents a Path-Assembled Closure Differential Mapping (PACDM) framework for modular closure resolution and kinematic reduction. Each closure element compares two ordered transformation paths with common endpoints, with their mismatch expressed through the logarithm on SE(3) and the corresponding Jacobian assembled from local transformation derivatives. Multi-path modules are constructed from a minimal set of pairwise closure elements, while rank-revealing analysis selects locally independent scalar constraints. A defect homotopy recovers closure-consistent passive coordinates from approximate estimates along a feasible and regular continuation path. At regular configurations, implicit differentiation yields the local active-to-passive differential mapping, which is subsequently used in a predictor-corrector continuation procedure for prescribed motion. The framework is evaluated on a seven-degree-of-freedom heavy-duty manipulator containing two-path and three-path closed-chain modules. Comparison with Simscape Multibody yields trajectory root-mean-square errors below 8.5 x 10^-10 rad, while predictor-corrector continuation is approximately 45.8 times faster than applying defect homotopy at every trajectory sample.

Underactuated robotic hands achieve adaptive and robust grasping with a reduced number of actuators, but predicting the stable equilibrium pose of the grasped object remains a significant challenge. This paper introduces a quasi-static analytical approach to assess passive stability in underactuated multi-finger hands. A novel three-finger hand architecture integrating a differential spring-loaded slider mechanism is introduced, enabling versatile and adaptive grasping. The study focuses on how the differential mechanism influences the overall grasp behavior and analyzes the effect of object size on the stable equilibrium configurations for two canonical grasp types: cylindrical and spherical.

Simulation of admittance-type models requires physically consistent dynamic models that are rarely available for off-the-shelf, everyday objects, limiting the fidelity of haptic interfaces that rely on such simulations. This paper presents the first complete workflow for producing physically consistent models of large real-world objects with various constraints and mechanisms, guaranteeing physical consistency of inertia and friction parameters. The workflow separates each object and identifies the handle and body in two stages, requiring no torque sensors at hinges, axles, or other constrained joints. Models are produced for a heavy, closer-actuated door and a wheelbarrow, representing objects of differing constraint types and model complexity. The door is modeled using four-bar linkage kinematics and a fluid dynamics-based lumped parameter model including opening, backcheck, swing, and latch zones. The wheelbarrow is modeled as a rigid body with a spherical wheel and no slip during rolling. Handle estimation RMS errors were below 0.64 N and 0.042 Nm across both objects. Door body estimation had RMS error of 2.19 Nm and wheelbarrow body estimation had RMS error of 6.77 Nm.

This paper addresses the sim-to-real gap in dynamics arising when a parallel-link mechanism is represented by a serial-tree surrogate in simulation. Conventional Jacobian-based state and torque mappings preserve consistency with the kinematic and virtual-work relations but do not account for the coordinate-induced redistribution of actuator inertia and damping and the linkage inertia omitted during serial-tree reduction. To address this gap, Simulator-Side System Normalization (S3N) is proposed to normalize the serial-tree simulator's effective dynamics while preserving its tree topology. S3N-Act incorporates actuator inertia and damping into the serial-coordinate dynamics through coordinate transformation, whereas S3N-Full restores residual linkage inertia by separately identifying actuator- and leg-level frequency responses. In the 2-DoF validation, S3N-Full reduced the joint-position and torque RMSEs by 80.9% and 82.1%, respectively, relative to the Jacobian-mapping baseline. During pitch-in-place motion, S3N-Act and S3N-Full reduced the RMSE of the ground reaction force norm by 65.1% and 62.4%, respectively. During circular locomotion, S3N-Full reduced the phase-averaged, command-normalized sim-to-real gap from 17.3% to 9.9%. These results show that simulator-side normalization improves motion- and force-level sim-to-real consistency. It enables policy training in a serial-tree framework with hardware-consistent dynamics that better represent the physical parallel-link mechanism.

A companion study introduced joint durability into the dimensional design of the Theo Jansen walking linkage and found its classical "holy numbers" Pareto-dominated, but it modelled the revolute joints as ideal, clearance-free pins, so its wear figures were relative rankings, not a prediction of in-service degradation. Here we relax that idealization. We build a forward-dynamic model of the Jansen leg in which a revolute joint becomes a clearance joint with a continuous normal contact law (Lankarani-Flores, hysteresis-damped) and Ambrosio friction, integrated as a constraint-stabilized differential-algebraic system, and couple it to the Archard law in a wear->clearance->impact feedback loop. Three findings emerge. First, neglecting clearance underestimates the peak joint load: the clearance model gives a peak contact force of ~104 N at the load-bearing pin against ~48 N for the ideal joint (~2x amplification), rising to ~426 N when two joints carry clearance at once. Second, the coupling is strongly impact-sensitive--single trajectories are non-monotonic and can reverse the design ranking, a chaos consistent with the literature--so designs must be compared statistically; over an ensemble of 16 randomized phases the optimized joint is robustly more durable, with per-cycle wear ~9-7x lower (peak force ~4x lower) at one clearance joint and still ~1.7x lower on both with two (p<0.01 throughout). Third, the wear is strongly non-uniform--it concentrates on a ~10 deg load arc--so assuming uniform clearance growth underestimates local clearance growth by ~36x. The clearance-free durability advantage thus survives the chaotic, multi-joint, non-uniformly-worn coupling in the ensemble mean. We deliver the first clearance-coupled forward-dynamic model of the Jansen leg and specify a falsifiable protocol to test each prediction.

The Jansen linkage is a single-degree-of-freedom planar leg mechanism whose eleven "holy numbers" were evolved by Theo Jansen to optimize the foot-path gait alone, with no regard for the wear of its revolute joints. This paper introduces a durability objective into the design of the Jansen leg. A parametric forward-kinematic model (two-circle-intersection solver), an inverse-dynamic model (constraint-Jacobian / Lagrange-multiplier formulation of a seven-body, ten-joint system, independently cross-verified by a reduced-DOF energy method), and an Archard wear model are coupled to evaluate, for any set of link lengths, both gait quality and the per-cycle sliding wear at every pin. Because the wear is computed on ideal, clearance-free revolute joints, the resulting wear figures are a relative comparative ranking rather than an absolute life prediction. A bi-objective problem -- composite gait error versus total joint wear, subject to step-length, ground-clearance, duty-factor and assembly constraints -- is solved with NSGA-II. Under the adopted gait metric the classical Jansen design is Pareto-dominated: for a representative design, link-length adjustments within +/-29% simultaneously flatten the stance (-28%), smooth the stance velocity (-58%) and reduce total joint wear by ~56%. A sensitivity study shows the wear advantage is robust across a crank-speed x payload envelope (48%-56%) and identifies the link lengths that most strongly govern wear. A variance-based global (Sobol) analysis confirms that two link lengths dominate the wear variance, and a Monte-Carlo manufacturing-tolerance study shows the wear advantage degrades gracefully under realistic fabrication error. The framework provides a practical route to longer-lived walking linkages and a baseline for future wear-clearance-impact coupled studies.

Robot learning has advanced rapidly in learning control, but learning the physical body of a robot remains much more difficult because jointly searching over design and control creates a very large combinatorial problem. Here, we present a data-driven framework for generating robot hands from human demonstrations. Instead of learning a complex controller together with each candidate design, we generate robot hand designs using the same simple control policy used after fabrication: matching fingertip positions through inverse kinematics. Using more than 4 million frames of human fingertip motion from everyday manipulation, our algorithm optimizes tree-structured robot hands to reproduce desired target motions. The framework produced both a 6-degree-of-freedom (DoF) general-purpose hand and lower-DoF task-specific hands with spatial four-bar mimic joints. To accelerate the search over designs, we trained a reinforcement-learning (RL) actor to propose good hand designs and joint angles, reducing search time from hours to minutes. We fabricated the mechanisms directly as one-piece articulated structures with print-in-place joints. In real-world experiments, the 6-DoF hand achieved highly accurate teleoperated fingertip tracking better than available commercial robot hands, whereas the specialized 3-DoF hands reproduced structured human and synthetic trajectories with reduced mechanical complexity. These results showed that large-scale human motion data can be used not only to train robot controllers but also as a reference for optimizing and generating the physical embodiment of robots.

In microrobotics, enhancing locomotion capabilities by increasing the degrees of freedom (DoF) of leg mechanisms under severe spatial constraints remains a significant challenge. Inspired by insect locomotion, this paper presents a novel micro-scale parallel leg mechanism with four degrees of freedom, and systematically analyzes its mechanical design, electrical system, and kinematics. The design incorporates two spherical five-bar linkages to achieve spatial motion within a parallel four-bar configuration. Furthermore, a concentric design strategy is employed to simplify the analytical solution of the leg kinematics. Due to the parallel system architecture, all actuators are located on the main body, substantially reducing the equivalent inertia of moving parts compared to traditional high-DOF leg structures. The total mass of the system is only 18.9 g, with an end-effector output force of approximately 0.5 N and a workspace exceeding 22255 mm3. Experimental results demonstrate that the proposed single-leg mechanism achieves excellent motion flexibility, highlighting its potential for micro bio-inspired robotics.

Planar path synthesis requires mechanisms whose coupler curves match a prescribed trajectory; the mapping from curve to linkage is inherently one-to-many across four-, six-, and eight-bar topologies. We address this design problem with simulation-grounded evaluation on a curated corpus of over one million mechanisms, reporting Chamfer distance and dynamic time warping after forward kinematics and geometric alignment. We formulate synthesis as conditional autoregressive sequence modeling: joint coordinates are uniformly quantized to tokens and generated by a decoder-only transformer with a variational-autoencoder (VAE) latent of the target curve and an explicit mechanism-type token. Training combines token cross-entropy with a Gaussian-smoothed bin auxiliary loss that respects ordinal structure among bins. At inference, a bounded latent-noise schedule decodes all mechanism types at each noise level; we retain the top five candidates by geometric error, yielding diverse accurate families without dataset lookup. On held-out tests, aggregate mean Chamfer distance is $0.0132$ and mean dynamic time warping is $0.153$; a latent $k$-nearest-neighbor baseline that conditions on training-set neighbor latents in VAE space achieves matched-topology mean Chamfer distance $0.0071$ and mean dynamic time warping $0.117$ using the same decoder.

Designing anthropomorphic robotic hands that balance functional dexterity with mechanical simplicity remains a significant challenge. Inspired by human hand synergies, this paper presents the SyLink Hand, an anthropomorphic dexterous hand that integrates biomechanical synergy principles with linkage-driven transmission mechanisms to achieve a high degree of anthropomorphism in appearance, kinematics, and functionality within a compact and cost-effective architecture. Biomechanical analysis of natural hand motions using motion capture gloves reveals strong kinematic correlations among hand joints, providing the basis for a simplified yet functional degree-of-freedom (DOF) configuration. Guided by these synergistic characteristics, optimized linkage mechanisms are employed to coordinate multiple joint motions and reproduce natural finger trajectories. A novel spherical four-bar linkage is further proposed to achieve decoupled flexion/extension (Flex/Ext) and abduction/adduction (Abd/Add) at the metacarpophalangeal joint within a compact form factor. The resulting prototype integrates 19 joints driven by 11 actuators, with a total mass of 520g and a manufacturing cost of approximately USD 400. Experimental evaluations demonstrate its human-like kinematic performance, high load-bearing capability, and versatile grasping and manipulation skills. These results validate that the synergy-inspired, linkage-based design effectively balances anthropomorphism, mechanical simplicity, and functional versatility, highlighting its potential for practical deployment in dexterity-demanding robotic applications.

This paper proposes, an improved version of the 3 in sewer pipe inspection robot equipped with an emergency evacuation mechanism. The low traction force and poor stepover capability, which were challenges of the first version, have been improved by simply connecting the propulsion units. The coupled propulsion units feature a differential mechanism capable of posture changes via a single wire, enabling adaptation to pipe diameter variations. To traverse obstacles like pipe joints, a control method was devised that detects obstacle contact through current load on the drive wheel motors and slackens the wire. This method was verified through simulated pipe experiments. Load comparisons were made using current waveforms applied to the drive wheels. Our proposed control method significantly improved the step-over capability of the new articulated robots.

Robotic locomotion can become efficient when mechanisms exploit passive dynamics, compliance, and resonance rather than track prescribed trajectories. This paper formulates natural locomotion as an exchange principle for systems whose motion is mediated by environmental constraints or interactions. A motion is natural when an internal oscillator returns periodically, the body pose drifts, and the mean Propulsion--Oscillator Exchange power (POE power) vanishes over one cycle. The selected family is a Natural Locomotion Manifold (NLM). We develop the conservative realization of this principle for continuous ideal environmental constraints: the constraints do no external work, total mechanical energy is conserved, and zero mean POE power is an internal exchange with the environment-mediated propulsive channel, not external energy input. The method is a closed/open construction. The propulsive channel is first closed to reveal an effective internal oscillator, organized by scalar action-angle structure in one effective degree of freedom or by nonlinear modal sectors in several degrees of freedom. The channel is then reopened, pose is reconstructed, and accepted cycles must preserve internal recurrence and zero mean POE power. We demonstrate the principle on two ideal nonholonomic no-slip systems: a Chaplygin-sleigh / pendulum-driven car and a three-body extension. In the scalar case, POE closure is equivalent to the missing internal return condition, giving a theorem-backed computation of the NLM family. In the multi-degree case, POE closure remains necessary but must be completed by modal identity, internal return, dynamics consistency, same fixed passive architecture, and nonzero displacement. Natural locomotion becomes a design question: which passive architectures support no, one, or several certified NLM families?

Biomimetic autonomous underwater vehicle (BAUV) with multi-link mechanism is widely used in aquatic life observation and environmental surveys due to its low power consumption and high maneuverability. An environmental survey requires a path following system that automatically follows specific points. However, the path following system of BAUV is limited, and its evaluation with multi-link mechanism robots has not yet been clarified. The path following system in BAUV requires prior simulation because the model differs depending on the type of biomimetics. In this study, we propose a path following system for BAUVs with a multi-link mechanism and evaluation in underwater simulation. In this result, it was possible to design a path following system suitable for BAUV, determine parameters using a simulator, and evaluate control methods.

We present a kinematic and transmission-aware design framework for a serial spherical mechanism with an additional translational degree of freedom for microsurgery. The first contribution is an analytical workspace formulation that provides geometric insight into reachable motion and enables rapid selection of rotation axis orientations without numerical optimization. The second contribution is a dynamics-informed methodology for mechanisms driven by self-locking transmissions, supporting evaluation of torque requirements for a prescribed workspace geometry. The framework is accompanied by an open-source software package for friction identification and inverse dynamics analysis. Experiments on a purpose-built robotic tool for vitreoretinal surgery validate the predictive capability of the models and demonstrate their practical utility for engineering design.

This paper presents a motion analysis framework for an athlete wearing sport-specific flexible prosthesis based on the soft-rigid hybrid-link system. Such a motion analysis is a challenging problem because we need to consider the interaction force between the rigid human skeleton system and a flexible prosthesis. However, most of human musculoskeletal models are based on the computation framework of a rigid-body multi-link system. Recently in soft robotics research field, fast and efficient modeling methods were developed for a flexible rod deformation, which allows us to build a hybrid-link system that integrates rigid-link and soft-bodies in a unified formulation. We apply inverse kinematics of the hybrid-link system to motion reconstruction from a motion captured data, and also present the estimation of the joint torques and ground reaction force by inverse dynamics. Through a human subject experiment, we show that the inverse dynamics achieved approximately 12% error on the ground reaction force estimation. Furthermore, we provide the muscle force estimation considering muscle amputation and interaction force with the prosthesis leg deformation.

Designing mechanical linkages involves combinatorial topology selection and continuous parameter fitting. We show that language models can systematically improve linkage designs through symbolic representations. Language model agents explore discrete topologies while numerical optimisers fit continuous parameters. A symbolic lifting operator translates simulator trajectories into qualitative descriptors, motion labels, temporal predicates, and structural diagnostics that models interpret across iterative design cycles. Across six engineering-relevant motion targets and three open-source models (Llama 3.3 70B, Qwen3 4B, Qwen3 MoE 30B-A3B), the modular architecture reduces geometric error by up to 68% and improves structural validity by up to 134% over monolithic baselines. Critically, 78.6% of iterative refinement trajectories show measurable improvement, with the system correctly diagnosing overconstraint (56.3%) and underconstraint (35.6%) failure modes and proposing grounded corrections. Models across all three families acquire interpretable mechanical reasoning strategies without fine-tuning, demonstrating that principled symbolic abstraction bridges generative AI and the numerical precision required for engineering design.

Quantitative analysis of the kinematic chain in sports motion is essential for performance evaluation and injury prevention. Conventional methods such as the kinematic-sequence (KS) and continuous relative phase (CRP) are confined to adjacent joint pairs and lack a unified framework for whole-body coordination, while segmental power-flow analysis requires force plates and inertial parameters that restrict it to laboratory environments. We apply Complex Hilbert Principal Component Analysis (CHPCA) separately to each motion phase (backswing and downswing) on markerless 3D pose estimation data, extracting the dominant whole-body phase pattern as a single complex eigenvector. The pipeline further includes a fully automatic signal-based phase segmentation (no priors on strike count or rest location) and an extension to 1,079 body-surface mesh vertices, so that the kinematic chain is represented as a continuous phase field across the body. On 14 hammer-striking trials of a single subject, the framework reveals (i) a trunk-anchored global phase architecture, (ii) a functional asymmetry between preparation and execution phases quantified by Mode-1 contribution (45.5% vs. 70.5%) and inter-trial Spearman consistency (0.38 vs. 0.58), and (iii) a consistent reorganisation across both skeletal joints and mesh vertices ($p < 10^{-10}$ on 1,079 vertices). As a methodological consistency check, pairwise phase differences from the Mode-1 eigenvector are compared against CRP on all 190 joint pairs by a permutation test ($ρ= 0.473$, $p = 0.0005$). A correspondence analysis between Mode-1 amplitude and kinetic-energy mobilisation variance further shows a strong positive correlation in the downswing ($ρ\approx 0.71$ on both skeleton and mesh) and no correlation in the backswing, indicating that the proposed framework bridges kinematic and kinetic descriptions of coordination through phase structure.

Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is becoming an important issue in human-machine interaction. Anticipating the dynamic behavior of variable topology mechanisms requires solving a non-smooth dynamic problem. The core challenge is a physically meaningful transition condition at the topology switching events. Such a condition is presented in this paper. Two versions are reported, one using projected motion equations in terms of redundant coordinates, and another one using the Voronets equations in terms of minimal coordinates. Their computational properties are discussed. Results are shown for joint locking of a planar 3R mechanisms and a 6DOF industrial manipulator.

The performance of legged robots depends strongly on both mechanical design and control, motivating co-design approaches that jointly optimize these parameters. However, most existing co-design studies focus on link dimensions and transmission ratios while neglecting detailed actuator design, particularly motor and gearbox parameter optimization, and are largely limited to serial open-chain mechanisms. In this work, we present a co-design framework for a planar closed-chain five-bar monoped that jointly optimizes mechanical design, motor and gearbox parameters, and control parameters for dynamic jumping. The objective is to maximize jump distance while minimizing mechanical energy consumption. The framework employs a two-stage optimization approach, where actuator optimization generates a mapping from gear ratio to actuator mass, efficiency, and peak torque, which is then incorporated into CMA-ES-based co-design optimization of the robot design and control parameters. Simulation results demonstrate an improvement of approximately 30.4% in jump distance and an 11.5% reduction in mechanical energy consumption compared to a nominal design, highlighting the effectiveness of the proposed framework for high-performance and energy-efficient planar jumping.

Underground mining robots are increasingly modeled for planning, operator training, and digital-twin workflows, where reliable actuator-level kinematics is needed to reduce hazardous in situ trials. Unlike typical open-chain industrial manipulators, representative mining machines are often linear-actuator-driven closed-chain mechanisms with planar four-bar linkages, making reusable kinematic modeling and real-time FK/IK solving challenging. We present \textit{\hl{MineRobot}}, an actuator-centered framework for modeling and solving the kinematics of this representative mechanism class. MineRobot introduces the Mining Robot Description Format (MRDF), a domain-specific representation that parameterizes mining-robot kinematics with native semantics for actuators and loop closures. It then contracts planar four-bar substructures into generalized joints and extracts, for each actuator, an Independent Topologically Equivalent Path (ITEP) classified into four canonical types. Based on this decomposition, per-type solvers are composed into a sequential forward-kinematics (FK) pipeline, while inverse kinematics (IK) is formulated as a bound-constrained actuator-length optimization solved by a Gauss--Seidel-style update scheme. By converting coupled closed-chain kinematics into small topology-aware solves, MineRobot reduces robot-specific hand derivations and supports efficient repeated FK/IK computation without treating each query as a full coupled constraint-solving problem. Experiments on representative underground mining robots demonstrate real-time FK performance and robust IK convergence within the tested operating ranges, supporting the use of MineRobot as an actuator-centered kinematic layer for planning, training, and digital-twin workflows.

Rigid link flapping mechanisms remain the most practical choice for flapping wing micro-aerial vehicles (MAVs) to carry useful payloads and onboard batteries for free flight due to their long-term durability and reliability. However, MAVs with these mechanisms require significant weight reduction to achieve high agility and maneuverability. One approach involves using single-DOF planar rigid linkages, which are rarely optimized dimensionally for high lift and low power, considering their sweeping kinematics and the unsteady aerodynamic effects. We integrated a mechanism simulator based on a quasistatic nonlinear finite element method with an unsteady vortex lattice method-based aerodynamic analysis tool within an optimization routine. We optimized three different mechanism topologies from the literature. Significant power savings were observed up to 34% in some cases, due to increased amplitude and higher lift coefficients resulting from optimized asymmetric sweeping velocity profiles. We also conducted a robustness analysis to quantify performance sensitivity to manufacturing tolerances. It provided a trade-off between performance and reliability and revealed the need for tight manufacturing tolerances and careful material selection. Finally, the analysis helped select the best mechanism topology, as we observed significant variation in sensitivity to manufacturing tolerances and peak input torque values across different topologies for a given design lift value. The presented unified computational tool can find application in flapping mechanism topology optimization, as it can simulate any generic single-DOF planar rigid linkage without supplying kinematics manually.