This paper presents KC3 Tensegrity Sim, an open-source python simulation framework for modeling class-k tensegrity structures with clustered-cable routing and cylindrical 2.5D geometries. In this work, a 2.5D tensegrity structure refers to a planar tensegrity topology whose nodes are constrained to lie on a prescribed three-dimensional cylindrical surface while retaining the connectivity of the original planar pattern. Rather than proposing virtual work as a new theoretical method, this study applies a virtual-work equilibrium formulation to integrate three modeling capabilities that are not jointly supported in existing tensegrity software: class-k connectivity, clustered cables routed through multiple nodes, and cylindrical surface-wrapping constraints. The framework represents tensegrity systems through declarative configuration files, assembles the corresponding equilibrium residuals numerically, and solves for static-equilibrium configurations in 2D, 3D, and cylindrical 2.5D settings. The framework is validated against a physical tensegrity structure and is intended to support early-stage design and configuration analysis of clustered and cylindrical surface-constrained tensegrity mechanisms, including wearable and morphing robotic structures.
Journal of Mechanisms and Robotics Open Issues
]]>We present a method to design the shape of a compliant mechanism to obtain large displacement at the output point in the desired direction while making the displacement in the orthogonal direction nearly zero. As the nonlinear constraint of the orthogonal displacement is challenging in gradient-based optimization, we adapt the interactive graphic statics method, which has been used so far to design only stiff trusses. We justify the use of truss models for compliant mechanism design by showing that there is no more than 20% deviation among truss, frame, and continuum models for the cases considered in this work. Furthermore, while the graphic statics method used for designing stiff trusses needs only the form diagram and a force diagram, our method requires two additional force diagrams. They correspond to the cases of unit virtual forces: one applied at the output point in the desired direction and the other in the orthogonal direction. The form diagram and three force diagrams enable the computation of individual contributions of truss members to the strain energy, output displacements in desired and orthogonal directions, and volume of the truss. Statically determinate and indeterminate truss topologies conceived intuitively or extracted from optimal continuum topologies are used for shape design. By interactively moving the vertices in one of the four diagrams and making corresponding updates in the others, we change the shape of the truss to achieve multiple objectives. The efficacy of the method is demonstrated with examples and preliminary validation using 3D-printed prototypes.
Journal of Mechanisms and Robotics Open Issues
]]>Forward kinematics is fundamental to robotic perception, planning, and control, yet it is often modeled as a deterministic mapping that neglects variability arising from sensor noise, actuation imperfections, calibration errors, and unmodeled dynamics. Existing uncertainty estimation methods either rely on local linearization, which is limited in capturing nonlinear and configuration-dependent effects, or use sampling-based techniques such as Monte Carlo simulation, which incur substantial computational cost. Learning-based alternatives frequently assume homoscedastic uncertainty and therefore fail to represent the state-dependent variability observed in real robotic systems. This article proposes a physics-informed framework for fast, configuration-dependent uncertainty quantification in robot forward kinematics using experimental data. A physics-based forward kinematics model is retained as the deterministic mean, while heteroscedastic residual uncertainty is learned as a configuration-dependent function from real-robot observations. The method is evaluated on a UR3 industrial manipulator and compared with homoscedastic and representative learning-based baselines. Experimental results demonstrate improved probabilistic calibration, reliable empirical coverage for both translational and rotational components, and microsecond-level central processing unit (CPU) inference, supporting real-time uncertainty-aware robotic applications.
Journal of Mechanisms and Robotics Open Issues
]]>Conventional mechanisms (linkages) are typically characterized by the presence of a frame that remains fixed with respect to an inertial reference system. In contrast, mobile robotic systems, including articulated robots, consist of assemblies of rigid bodies that are free to undergo planar motion. The integration of these two paradigms leads to a class of mechanical systems in which a linkage structure is itself capable of moving on the plane. Such systems are hereafter referred to as mobile-linkage robotic systems (MLRSs). In an MLRS, the wheels not only provide locomotion but also actively participate in altering the kinematic configuration of the mechanism, resulting in a coupling between mobility and reconfiguration. This article provides a theoretical framework of general validity, applicable to a broad class of MLRSs, independently of their specific mechanical realization. In particular, both direct and inverse kinematic formulations are provided.
Journal of Mechanisms and Robotics Open Issues
]]>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.
Journal of Mechanisms and Robotics Open Issues
]]>This article focuses on experimental tests of three closed-loop control strategies: sliding mode control (SMC), model predictive control (MPC), and proportional-integral-derivative (PID) control with linearization applied to a tensegrity medical device, with the purpose of comparing them. The mechanism is designed to be part of a medical device for transcutaneous puncture applications where it is necessary to achieve a desired system orientation, adjust its stiffness, and ensure robustness against external disturbances such as natural human body movements. The performance of the three control strategies is compared for the tasks of trajectory tracking, stiffness adjustment, and robustness against external disturbances.
Journal of Mechanisms and Robotics Open Issues
]]>Powered two-degree-of-freedom (2-DOF) ankle-foot prostheses have distinct requirements for dorsiflexion/plantarflexion (DP) and inversion/eversion (IE) actuation. However, current designs rely on mechanically coupled DP and IE actuation with complex transmission stages. Thus, we present a proof-of-concept 2-DOF ankle-foot mechanism with unloaded kinematic validation using two simple and decoupled transmission stages. A ball-screw mechanism drives DP and a gear-and-chain mechanism drives IE, each constituting a single-transmission stage. A weighted mechanical complexity metric benchmarks this proof-of-concept architecture against five existing 2-DOF designs. Kinematic tracking is validated in Simscape Multibody simulation against gait data, and axis decoupling is experimentally confirmed using a 10-camera infrared motion capture system. The proposed design uses only two transmission stages instead of the four to six stages found in other alternatives. Experimental validation yields a DP-IE Pearson correlation coefficient of −0.018, confirming near-complete mechanical decoupling. The design achieves a DP range of −28.9 deg to 12.0 deg and an IE range of −22.5 deg to 22.5 deg, meeting daily-living motion requirements for level-ground walking. The unloaded kinematic decoupling validations provide a basis for further development of 2-DOF powered ankle-foot prostheses implementing our design with reduced transmission complexity.
Journal of Mechanisms and Robotics Open Issues
]]>Designing legged robots for running in complex, unstructured environments requires systematic formulations of heterogeneous, multidomain constraints and variables, including component choices, geometric choices, controller profiles, and touchdown conditions, which remains underexplored for small-scale (10–500 g) legged robots. At these scales, identifying feasible and robust running solutions becomes increasingly difficult—especially on rough terrain—due to limitations in physical parameters, reduced sensing capabilities, lack of a priori terrain knowledge, and limited onboard computing. This article introduces an optimization formulation and solution framework that concurrently designs the physical system (morphology) and controllers for small-scale robots that are abstracted as torque-driven spring-loaded inverted pendulums (TD-SLIP). A set of constraints is defined to promote a symmetric gait, bounding touchdown conditions and vertical/horizontal displacements, which, along with the objective function, promote a greater number of gait cycles. Motion control is achieved with a combination of optimally tuned Proportional-Integral-Derivative (PID) control of the stance phase and optimizing the motor-actuation period for the flight phase. Optimization is performed using a standard mixed-discrete Particle Swarm Optimization algorithm. The optimized design on the flat terrain achieved 19 stable gait cycles. Initializing with the flat-terrain optimized design is found to be uniquely helpful in successfully driving the optimization search over the design space for rough-terrain scenarios, while achieving at least 14% better gait performance compared to the flat-terrain design. Evaluated over a large set of unseen rough terrains, the corresponding optimized designs demonstrate stable gaits with 8 or more cycles in most cases.
Journal of Mechanisms and Robotics Open Issues
]]>Motion planning and control for robotic manipulation of deformable linear objects (DLOs) necessitate computationally efficient and sufficiently accurate estimation of the DLO shape. Ideally, such an estimation should be able to reconstruct the deformation field from the pose of the terminal ends of the DLO only, which is particularly relevant for dual-arm manipulation. Numerical shooting and collocation methods accurately solve the associated boundary value problem, but are not applicable in time-critical conditions. In this article, a highly efficient algorithm is introduced for shape reconstruction of DLOs undergoing large deformations. The method yields an explicit analytic representation of the displacement field. DLOs are modeled as Kirchhoff rods since shear and compression can be neglected for the majority of relevant objects. The method is derived from a third-order approximation of the exact solution. Assuming homogeneous material and constant cross section, the shape estimation problem is reduced to a purely kinematic problem, which does not need material parameters. Unlike other approaches that minimize the overall elastic potential and respectively solve the corresponding variational boundary value problem, the presented method derives from minimizing the terminal strains. The solution method shows an excellent accuracy while being highly efficient at the same time. The result is equally relevant for continuum robots.
Journal of Mechanisms and Robotics Open Issues
]]>Passive stiffness modulation is essential for compliant robotic systems in dynamic and uncertain environments, where rigid actuators or constant stiffness designs are often insufficient to ensure safety and adaptability. This article presents the design, modeling, optimization, and experimental validation of a load-dependent contact-aided compliant joint (LCCJ) that passively modulates stiffness in response to external torque. An integrated design pipeline is established, which bridges a high-fidelity analytical framework with a physically motivated optimization strategy. The framework combines a chained pseudo-rigid-body model (CPRBM) with Karush–Kuhn–Tucker (KKT) conditions to describe the complex beam-boundary interactions. Using the distinct deformation regimes of the mechanism, the pipeline employs a two-stage optimization strategy to precisely map the desired stiffness modulation back to the physical geometric parameters. Simulation results demonstrate that, across the benchmark and optimized-design validation cases, the model predictions agree closely with finite element analysis (FEA), with maximum relative errors in the torque-deformation response of 4.02% and 3.18% in the pre- and post-contact regions, respectively. Experimental validation confirms the effectiveness of the proposed design; compared to the FEA predictions, the experimental results exhibit relative errors below 2.6% in the precontact region and 5.22–6.21% in the post-contact region. The LCCJ offers a compact and monolithic solution for passive stiffness modulation in compliant joint applications.
Journal of Mechanisms and Robotics Open Issues
]]>