Management Science

The dynamic transmission error of the joint RV (rotating vector) reducer is one of the important factors affecting the positioning accuracy of industrial robots. However, the current studies on the transmission accuracy characteristics of RV reducers are based on the equal speed driving condition, which neglects the impact of the transmission error generated by the joint RV reducer on the positioning accuracy when the robot is in the start-stop variable speed phase. This study carries out an in-depth analysis of the dynamic transmission accuracy characteristics of joint RV reducers of industrial robots under variable-speed working conditions. Two typical mathematical models of variable-speed drive laws are constructed, and a multibody dynamic model of the RV reducer that takes into account the geometric errors of typical components is established, aiming to more accurately simulate the operating state of the RV reducer under actual working conditions. To confirm the accuracy of the theoretical RV reducer contact dynamics model, the dynamic transmission error test of the RV reducer under equal-speed conditions is carried out. The results show that the dynamic model can better reflect the actual transmission characteristics of the RV reducer. Thereafter, based on the theoretical model, the effects of different driving laws on the dynamic transmission error of joint RV reducers are analyzed in depth. The results of the study show that the transmission error of the RV reducer under variable speed drive is significantly larger than that under equal speed drive. Moreover, angular acceleration and load inertia are the main factors affecting the transmission error of RV reducers for industrial robot joints.

Abstract Accurate and robust modelling of muscle paths is crucial for predicting human movement. Traditional methods often rely on simplified straight-line representations and manual specifications of via-points and wrapping surfaces, which may lead to inconsistent and unrealistic muscle paths The discrete geodesic Euler–Lagrange (DGEL) method identifies geodesics with minimal curvature trajectories that adhere closely to anatomical constraints. Embedding DGEL into an optimisation problem with a specific objective function has the potential to identify muscle paths with smooth changes in muscle length over the course of the motion, thereby avoiding abrupt muscle discontinuities. This study aims to investigate the performance of the DGEL method. We developed multibody models with increasing complexity (i.e. a static arm model, a kinematic elbow model and a kinematic shoulder model) and investigated different scenarios, such as muscle attachment modifications, simulation of diverse motions and extreme ranges of motion. We performed a comparative analysis between the geodesic model and the open-source OpenSim framework, with validation against experimental data to assess physiological plausibility. Our findings reveal that the DGEL method overcomes limitations inherent in traditional approaches, including discontinuities and incorrect wrapping surface interactions. For the static arm model, the DGEL-computed muscle length showed a closer match to ground truth compared to OpenSim. In the elbow model, the DGEL method eliminated unphysiological muscle path discontinuities. In the shoulder model, the DGEL method was validated across three different motions against experimental muscle moment arms, achieving great accuracy and superior robustness in handling complex muscle paths. This method effectively addressed common pitfalls in muscle path modelling, such as bone penetrations and erratic trajectories. Future work will further validate the DGEL method across diverse real-world applications and optimise its performance through advanced objective functions. The DGEL approach represents a significant improvement in the accuracy and robustness of muscle path modelling, advancing the field of biomechanics and musculoskeletal modelling.

Abstract In recent years, colonic capsule endoscopy has become available in clinical practice as an alternative modality to colonoscopy. However, it faces challenges such as prolonged examination time and the absence of clinician navigation. Leveraging their pioneering work in the field of vibro-impact self-propulsion technique for gastrointestinal endoscopy, Zhang et al. (IEEE Robot. Autom. Lett. 8:1842–1849, 2023) developed a novel, untethered, self-propelled, endoscopic capsule robot, with the aim of providing a new means of examining bowel cancer in real time. To evaluate and optimize the passage of this capsule robot self-propelling in the large intestine, this work adopts multibody dynamics analysis and experimental investigation to study the robot’s dynamics and its interaction with the intestinal environment. Considering the complex anatomy of the large intestine, containing different sections, e.g., cecum, ascending, transverse, descending, and sigmoid colon, and variations of the haustra, e.g., with various radii, lengths, and heights, the robot was driven by the square-wave excitation of an inner mass interacting with the capsule body and tested on a real porcine colon. The robot’s driving parameters, including the excitation frequency, amplitude, and duty cycle, and the dimensions of the haustra are the two main factors influencing the robot’s progression in the intestine. By comparing with the experimental results, the proposed multibody dynamics model developed using MSC Adams can estimate the movement of the capsule robot and the intestinal resistance quantitatively. Extensive numerical and experimental studies suggest an excitation frequency of 60 Hz and a duty cycle of 0.4 as the optimal parameters for driving the robot, and the longer the haustral length is, the faster the robot passes through. These results ensure the validity of the proposed multibody dynamics platform, which can be used by robotic engineers for developing medical robots for intestinal examinations.

Abstract This work presents a new formulation for flexible fluid-conveying pipe elements based on the widely used floating frame of reference formulation. The elements can be used as a tool for the analysis of flexible multibody systems that contain fluid-conveying pipes, as it is well known that the movement of the fluid can influence the behavior and stability of such systems. The pipe defines a control volume through which the fluid, which is considered to be a moving mass, axially flows. The velocity of a material point of the fluid is therefore a material derivative of its position, representing the large rigid movement and small elastic deformation of the pipe along with the velocity of the fluid with respect to the pipe. The equations of motion are derived through the principle of virtual work, spatial discretization by finite element interpolation functions, and model reduction. A simplification of the consistent equations of motion is proposed, which avoids the use of inertia shape integrals and reduces the effort required to implement the developed fluid-conveying pipe elements in existing multibody software. The developed elements are validated by simulation of a straight cantilevered pipe and a curved pipe constrained on one end by a hinge. A simulation of a concrete printing system illustrates the straightforward incorporation of the elements in larger multibody systems.

The problem of multi-point collision and contact in multi-legged robots involves complex dynamics with multiple closed loops, variable topology, and numerous contact points, making simulations challenging. Additionally, Zeno behavior—characterized by an infinite number of discrete transitions within a finite time—is likely to occur, reducing computational efficiency and potentially causing simulations to stall. This paper establishes a linear complementary dynamic model to study the collision and contact problem of multi-legged mobile robots. For the uncertainty of multi-point collision and contact, we use sets and transformation matrices to represent the number and position changes of the points that collide or contact with the ground. This paper separately studies the problems of multi-point collision and multi-point continuous contact and considers the coupling effect of collision and continuous contact. A new criterion to determine the state of continuous contact is proposed, and modifications are made to the relevant linear complementary equations to prevent the Zeno behavior. Finally, several numerical examples are provided to verify the effectiveness of the method.

For suppressing multidimensional vibration effectively, the multidimensional vibration isolator based on parallel mechanism considering interval joint clearance is proposed. The kinematics and dynamics of the isolator are established respectively. The contact force generated due to interval joint clearance is modeled respectively by the Lankarani–Nikravesh (L-N) model and the modified Coulomb friction force model. Furthermore, the dynamics of the isolator with interval joint clearance are obtained by the first order interval perturbation method. The upper and lower bounds of vibration isolation performance are calculated, which indicates the isolator with interval joint clearance inhibited external vibration in time and frequency domain respectively. The vibration isolation performance is most sensitive in pitch (around $x$ ) direction due to the existence of interval joint clearance. The non-probabilistic reliability model of the isolator is proposed by the shortest distance method, and the non-probabilistic reliability index is investigated in each isolation direction with interval joint clearance. The reliability index of the isolator exhibits a quasi-stable area in horizontal (in $x$ ) and pitch (around $x$ ) directions, which implies the reliability index is not sensitive to joint clearance variation in a certain perturbation range. The proposed vibration isolator with interval joint clearance is fabricated, and the vibration isolation experiment is conducted. The experimental results are generally consistent with the theoretical results, which indicates the correctness of the analysis.

The wheel–soil interaction has great impact on the dynamics of off-road vehicles in terramechanics applications. The soil contact model (SCM), which anchors an empirical method to characterize the frictional contact between a wheel and soil, has been widely used in off-road vehicle dynamics simulations because it quickly produces adequate results for many terramechanics applications. The SCM approach calls for a set of model parameters that are obtained via a bevameter test. This test is expensive and time consuming to carry out, and in some cases difficult to set up, e.g., in extraterrestrial applications. We propose an approach to address these concerns by conducting the bevameter test in simulation, using a model that captures the physics of the actual experiment with high fidelity. To that end, we model the bevameter test rig as a multibody system, while the dynamics of the soil is captured using a discrete element model (DEM). The multibody dynamics–soil dynamics co-simulation is used to replicate the bevameter test, producing high fidelity ground truth test data that is subsequently used to calibrate the SCM parameters within a Bayesian inference framework. To test the accuracy of the resulting SCM terramechanics, we run single wheel and full rover simulations using both DEM and SCM terrains. The SCM results match well with those produced by the DEM solution, and the simulation time for SCM is two to three orders of magnitude lower than that of DEM. All simulations in this work are performed using Chrono, an open-source, publicly available simulator. The scripts and models used are available in a public repository for reproducibility studies and further research.

Abstract Flexible body dynamics simulations are powerful tools to realistically analyze vehicles, machines, mechanics, etc. However, the inherently nonlinear governing equations often require tailor-made and computationally expense solution strategies. Employing artificial neural networks for forward dynamics analyses of flexible bodies may be not only useful as a model reduction tool, since evaluating a network is frequently faster compared to solving physics-based models, but also to enhance models with experimental data. In this realm four primary strategies have emerged: (i) Incorporating time as an input to the artificial neural network to predict the desired solution variables at that specific time. (ii) Utilizing an entire time series as input, the network generates the corresponding time series of the desired solution variables in a single pass through the artificial neural network. (iii) Employing an artificial neural network to advance one time step into the future using the states as input. (iv) Leveraging the artificial neural network solely for learning the equations of motion or energetic quantities, e.g., Lagrangian/Hamiltonian, coupled with standard techniques from analytical dynamics and time integration. Approaches (iii) and (iv) can be considered advantageous owing to their inherent physics-informed nature, greater flexibility in adopting varying time steps, and ease of integration with classical simulation techniques. This contribution, therefore, presents a method to predict flexible body dynamics one step at a time using two complimentary artificial neural networks. One network predicts the equations of motion relationship between positions, velocities, and accelerations, while a second network or numerical integrator propagates the system states forwards in time. This work demonstrates the feasibility of the developed approach on the testcase of a flexible beam. Various parameter studies and alternative solutions are presented to highlight the performance of the developed approach. The robustness and ability to extrapolate are also explored to determine the practical viability of this solution. The intention of this single-body work is to enable the future embedding in a multibody context.

This paper proposes a feedback control technique for path and trajectory tracking on multi-input, multi-output nonminimum phase underactuated multibody systems and applies it to a spatial gantry crane moving a double pendulum. The two links forming the double pendulum are connected in series and the desired output of the system is the tip of the second link. This output selection yields to a nonminimum phase system, which is a class of dynamical systems that are particularly challenging from the control design perspective. In this paper, an enhanced formulation of Model Predictive Control is proposed to solve the output trajectory tracking problem by embedding the dynamics of the spatial reference trajectory within the optimization process performed at each time step. The proposed control technique is formulated considering two different scenarios: the case of torque-controlled (i.e., current-controlled) actuators, and the case of position-controlled actuators. The latter is unusual in the field of MPC and is suitable for industrial applications where proprietary controllers are adopted. Numerical validations show negligible contour and tracking errors during the execution of the desired trajectories, with low computational effort.

AbstractWhile designing rehabilitation exoskeletons is often realised based on experience and intuition, many processes can be computer-aided. This gives the opportunity to design lighter and more compact constructions. Hence, the devices can be fully wearable and have a wider range of motion. So far, mainly topology optimisation and parametric dimensional optimisations have been used for that. The presented study addresses the problem of automatic selection of the driving systems for exoskeletons. It consists of the literature review of the components used to actuate the joints of such constructions, optimisation algorithm development, and a case study on the EXOTIC exoskeleton. The method includes building a database of motors and gearboxes, computing inverse kinematics of a system to obtain angular trajectories from the task-oriented paths, iteration computing inverse dynamics to compute required torque and the search for the optimal solution according to the defined goal function. This approach enables single joint and multijoint optimisation, with the custom goal function minimising optionally masses, diameters or widths of the selected driving systems. The investigation consists of the 28 simulation trials for EXOTIC exoskeleton to compare results obtained for different aims. Moreover, to visualise the effect, the 1st DOF driving mechanism is redesigned to obtain its minimum width based on the optimisation results. The optimal choice reduced the actuation mechanism mass by 15.3%, while its total dimensions by 17.5%, 8.5% and 26.2%, respectively. The presented approach is easily transferable to any other active exoskeleton and can contribute to designing compact and lightweight constructions. This is particularly important in assistive rehabilitation and can also be used in industrial assistance processes.

This study presents a novel Forward Dynamic approach that integrates a Genetic Algorithm (GA) to generate and optimize gait patterns with Inverse Dynamics analysis, tailored to individual users in the robot-assisted training platform. The resulting trajectories provide gait-trajectory planning using the developed gait-pattern simulator, enabling medical personnel to select customized tasks and training trajectories for users based on their training goals, subsequently transferring user-specific parameters to the exoskeletal robot for rehabilitation/training. By leveraging biomechanical data as reference (joint torque and force) from the Inverse Dynamic analysis, the method foregoes the necessity for experimental data, directly predicting joint angles and positions. To ensure the validity of the proposed method, we used a combined approach of numerical analysis and comparison with motion-capture data. This evaluation aimed to assess how closely the simulated results resembled real human walking motion for the lower-extremity joints.

Lubricated translational joints are extensively utilized in power equipment. Due to the presence of clearance, the moving mass exhibits transverse motion within the guide rail in addition to its reciprocating motion. This transverse motion significantly influences the friction, wear, and service life of the friction pair. In this process, multi-physics factors such as fluid lubrication, structural deformation, and frictional heat generation interact with each other, making the tribo-dynamics characteristics very complex. In the current study, a new thermal-fluid-solid coupled method for modeling the tribo-dynamics of translational lubricated joints is presented, and it is applied to the crosshead slider-guide friction pair in marine engines. Research results show that the tribo-dynamics characteristics of the slider predicted by the model is consistent with the experimental ones, the correctness of the model is verified. The frictional heat generation has little effect on the tribo-dynamics characteristics of the crosshead slider under the rated operating conditions. However, the structure deformation induced by the external load intensifies the transverse motion of the crosshead slider. Compared with the model that ignored the deformation, the transverse displacement can be increased by 30%, which indicates that it is necessary to consider the multi-physics coupling effect.