Forward Dynamic Analysis Research Articles

Unified dynamics analysis of parallel manipulators: A joint-based approach and generalized inertia constraint matrix for parallel manipulators (GICM-P) framework

Parallel manipulators, a distinctive subset of closed-loop multi-body systems, are in high demand due to their precision-centric applications. This research introduces a unified approach to tackle both inverse and forward dynamic analyses of parallel manipulators, rooted in joint-based principles. The methodology dissects a given parallel manipulator into symmetric open-loop subsystems and a mobile body within either a planar or spatial context, depending on the manipulator’s nature. Conventional practices, involving the introduction of joint cuts at relevant locations, are employed to partition the system into multiple open-loop subsystems. Subsequently, the joint coordinate-based approach, typically applied to open-loop systems such as industrial manipulators, is utilized to derive solutions. In particular, this approach focuses on forward dynamics by introducing the generalized inertia constraint matrix for parallel manipulators (GICM-P), a concept built upon the authors’ prior work, originally addressing the GICM for general closed-loop systems. Notably, GICM-P aligns conceptually with the operational space inertia matrix (OSIM) designed for closed-loop systems elsewhere. However, unlike OSIM, which requires mapping joint-space inertia to operational-space inertia, GICM-P leverages acceleration-level constraints between subsystems and the moving platform through straightforward matrix operations. GICM-P offers a deeper understanding of the physics of the problem compared to OSIM, primarily due to its ability to explicitly express subsystem-level interactions via various block matrices – an aspect not previously documented. The paper provides explicit numerical values for GICM-P in the context of a spatial six degrees of freedom (6-DOF) Stewart platform and a planar 3-DOF parallel manipulator along with interpretations.

A gradient based numerical algorithm to solve inverse dynamic viscoelastic problems of multi-variable identification

A gradient based numerical method is put forward to solve the inverse dynamic viscoelastic problem with multi-variable identification for the constitutive and TKBC (third kind boundary conditions) related parameters. A three parameter model is employed to describe the time dependent TKBC concerned with structural interaction, and is formulated in the forward and inverse dynamic viscoelastic analysis. In addition to the reliable platform provided by TPAA-SBFEM to gain the solution of forward problems, a piecewise recursive adaptive algorithm is developed to obtain the derivatives required in the sensitivity analysis, which is able to provide a stable temporal solution accuracy for different step sizes. SBFEM (Scaled Boundary Finite Element Method) is stressed in the structural analysis with its own advantages, such as the efficient and convenient treatment of stress singularity problem and flexibility of mesh generation with polygonal elements and image based quadtree gridding. The inverse problem of identification is solved by the Levenberg-Marquardt method, and the regional inhomogeneity, crack, initial guess, location/number of measurement points, material contrast ratios, and noisy data are taken into account. Numerical examples are provided to verify the proposed approach, and the satisfactory results are achieved.

Linearization-based state-transition model for the discrete extended Kalman filter applied to multibody simulations

This study investigates the discrete extended Kalman filter as applied to multibody systems and focuses on accurate formulation of the state-transition model in the framework. The proposed state-transition model is based on the coordinate-partitioning method and linearization of the multibody equations of motion. The approach utilizes the synergies between the integration of states and estimator covariances without overly simplifying the integrator structure. The proposed method is analyzed with a forward dynamics analysis of a four-bar mechanism. The results show that the stability of the state-transition model in the forward dynamics analysis is significantly enhanced with the proposed method compared with the forward Euler-based methods. The computational efficiency of the novel method was significantly lower in comparison to forward Euler-based methods, which was found to be mainly due to the computation of the Jacobian matrix of the nonlinear state equation. However, the increase in computational cost can be considered acceptable in Kalman-filtering applications, where the exact Jacobian of the state equation is needed.

Sarcopenia: Body Composition and Gait Analysis

BackgroundAge-induced sarcopenia negatively affects walking stability and increases the risk of falls, which is the leading cause of accidental death in the elderly.ObjectiveThis study aimed to analyze and contrast body composition and gait characteristics in those with sarcopenia in relation to healthy controls to shed some light on the prevention of falls in elderly patients with sarcopenia.Materials and MethodsIn this study, 68 community dwellers were scanned by the Hologic QDR-4500A Dual-energy X-ray absorptiometry (DXA). The appendicular lean mass index (ALMI) results were used to distinguish the normal participants from those with sarcopenia: 24 in the sarcopenia group, and 44 into the normal group. The participants were asked to undergo gait analysis on a plantar pressure measurement system. Statistical analysis was conducted to contrast both groups' gait and butterfly parameters from their gait test, and then a gait forward dynamics method was performed to quantify the analysis for both groups.ResultsThe ALMI of the female was not related to their age (r = 0.06) while that of the male was weakly related (r = 0.17). Body mass index (BMI) from both groups was normal, although with a statistically greater BMI from the normal group compared with sarcopenia (p < 0.001). Greater values and significant differences were found in step length and stride length from the normal elderly group (p < 0.01), and so was the length of the gait line and single support line (p < 0.05). Gait forward dynamics analysis results showed no motor neural or musculoskeletal disorders in their gait performance from the sarcopenia group.ConclusionFor the elderly, age did not largely affect the ALMI, BMI, or T-score, but BMI and ALMI were strongly correlated. In this study, significant differences were found in certain gait parameters between the elderly with sarcopenia and the normal elderly, which were related to absolute muscle strength, suggesting that sarcopenia was a disease mainly caused by decreased muscle mass. In addition, when abnormities were identified in step length, stride length, length of gait line, or length of single support line, it is proposed to take a DXA scan to confirm whether the elderly suffer from sarcopenia.

Comparison of several muscle modeling alternatives for computationally intensive algorithms in human motion dynamics

Several approaches are currently employed to address the predictive simulation of human motion, having in common their high computational demand. Muscle modeling seems to be an essential ingredient to provide human likeness to the obtained movements, at least for some activities, but it increases even more the computational load. This paper studies the efficiency and accuracy yielded by several alternatives of muscle modeling in the forward-dynamics analysis of captured motions, as a method that encompasses the computationally intensive character of predictive simulation algorithms with a known resulting motion which simplifies the comparisons. Four muscle models, the number of muscles, muscle torque generators, muscular synergies, and look-up tables for musculotendon lengths and moment arms are considered and analyzed, seeking to provide criteria on how to include the muscular component in human multibody models so that its effect on the resulting motion is captured while keeping a reasonable computational cost. Gait and vertical jump are considered as examples of slow- and fast-dynamics motions. Results suggest that: (i) the rigid-tendon model with activation dynamics offers a good balance between accuracy and efficiency, especially for short-tendon muscles; (ii) including muscles in the model leads to a decrease in efficiency which is highly dependent on the muscle model employed and the number of muscles considered; (iii) muscle torque generators keep the efficiency of skeletal models; (iv) muscular synergies offer almost no advantage for this problem; and (v) look-up tables for configuration-dependent kinematic magnitudes have a non-negligible impact on the efficiency, especially for simplified muscle models.

Forward dynamic analyses of cable-driven parallel robots with constant input with applications to their kinetostatic problems

Forward dynamic analyses of cable-driven parallel robots (CDPRs) are performed accounting for the spatial motions of the cables while considering their mass, sag, elastic and damping properties. The winches feeding the cables are considered stationary. An efficient recursive forward dynamic algorithm is developed to perform the extremely demanding computations. As a part of this work, a solution to the kinetostatic problem of CDPRs is proposed, wherein starting with a non-equilibrium pose, the CDPR is allowed to evolve dynamically until attaining an equilibrium. This idea is demonstrated on a spatial 6-3 CDPR, the feed-support system of the Five-hundred-meter aperture spherical radio telescope (FAST), as well as the 8-8 CDPR, CoGiRo. Dynamic simulation of this nature using a full-scale model of the FAST manipulator is reported for the first time. The results are validated numerically, as well as against existing models, wherever feasible. Challenges involved in the modelling and computations at such a scale and the corresponding remedies are elaborated.

Forward dynamics analysis of origami-folded deployable spacecraft structures

A fast dynamics model that captures the deployment dynamics of self-actuated, origami-inspired, folded planar spacecraft structures is desired for design and verification applications. In this paper, a general simulation framework for numerically generating the equations of motion of any structure that complies with a set of pattern assumptions is presented. The framework is built through application of the articulated body forward dynamics algorithm and the tree-augmented approach for closed-chain forward dynamics. These are multi-body dynamics approaches developed in the literature for complex robotic manipulator systems. Unique adaptations are required to address the highly constrained nature of a folding structure. This solution is desirable due to the computational efficiency of the base algorithms and the ability to analyze multiple systems without reformulation of the core dynamics algorithm. Baumgarte stabilization techniques are applied to address constraint violations, but are found to be a continuing challenge for folding structures with several closed-chains.

Leg-orthosis contact force estimation from gait analysis

Spinal cord injured subjects with hip flexion ability may often walk with the help of orthosis and crutches. Typically, the orthotic devices are attached to the legs by means of several braces. Excessive pressure in such contacts may lead to skin wounds and to subsequent loss of adherence to the use of the orthoses. Since contact pressures are related to contact forces, estimation of the leg-orthosis contact forces is relevant to assess the suitability of an orthotic device for a specific subject, or to redesign the braces for pressure reduction. In this paper, a procedure to estimate such contact forces from simple gait analyses is proposed. It consists of building computational multibody models of subject and devices, and running a forward-dynamics analysis of the orthoses in which the captured motion of the subject is prescribed. At least one force/torque sensor per orthosis is required to calibrate the model. In this case, an extensometry-based load cell was used for such purpose. Results showed that, once calibrated, the model was able to reproduce torque sensor measurements for different motions.

Inverse and forward dynamics of a 4RSS+PS parallel manipulator with one infinite rotational motion

ABSTRACT Modelling and dynamic analysis of a novel four degrees of freedoms (DOFs) parallel manipulator (PM) with 4RSS+PS topology is conducted in this paper. The letters R, S and P denote revolute joint, spherical joint and prismatic joint, respectively, and underline denotes an actuated joint. The proposed manipulator has three rotational and one translational DOF (3R1T), while one of the rotational DOFs around the direction of translational DOF is free of limitation. In addition to the inverse kinematic, velocity and acceleration analyses, a computationally efficient scheme based on the principle of virtual work is presented to derive a closed-form dynamic equation of the 4RSS+PS PM. Then, the dynamic equation is applied for the inverse and forward dynamic analyses of the manipulator. Numerical examples are also studied with Matlab software and its SimMechanics toolbox to demonstrate correctness and efficiency of the presented dynamic modelling.

Workspace analysis and trajectory tracking of a planar hybrid manipulator with ball screw feed drive

The hybrid manipulators have benefits of both serial as well as parallel manipulators. In this paper, a planar hybrid manipulator with six degrees-of-freedom is proposed; it consists of two parallel manipulators each having three degrees-of-freedom. The models for forward and inverse dynamic analysis of this manipulator are presented with bond graph approach. The actuators of the manipulator have ball screw feed drive mechanism to convert rotary motion into linear motion. There are basically three problems addressed in the paper. First, the models are simulated for trajectory tracking of a semi-circular path traced by the lower manipulator initially and then tracking of another semi circular path by upper manipulators. The second problem addressed is to develop the bond graph model of the hybrid manipulator with proportional control to reach a desired position from an initial position with an unity slope after few seconds. Finally, workspace analysis for given semi-circular trajectory is done with calculation of area of the workspace of lower, upper and hybrid manipulators. It is observed from the simulation that the response follows the desired trajectory within the permissible limit. The result indicates that manipulator follows nearly tangential path. It is seen from the result that the desired trajectory lies within the workspace boundary.

A comparative study of the configuration-space and actuator-space formulations of the Lagrangian dynamics of parallel manipulators and the effects of kinematic singularities on these

This paper studies the configuration-space and the actuator-space variants of the Lagrangian formulation of dynamics of parallel manipulators. In particular, the effects of the gain-type singularity and the configuration-space singularity on the forward and inverse dynamic analyses using these formulations are studied in detail. A condition for kinematic consistency at a gain-type singularity is established. The formulations are implemented on a planar five-bar manipulator and a bi-planar Stewart platform manipulator. Extensive numerical simulations augment the analytical developments in the understanding of the dynamic behaviour of the manipulators, in both the singular and the non-singular cases.

Skeletal-level control-based forward dynamic analysis of acquired healthy and assisted gait motion

Gait analysis is commonly addressed through inverse dynamics. However, forward dynamics can be advantageous when descending to muscular level, as it allows activation and contraction equations to be integrated with motion thus providing better dynamic consistency, or when studying assisted gait, as it enables the estimation of the interaction forces between subject and devices even if the motion capture process doesn’t provide enough resolution to distinguish the motions of limb and device. Control-based methods seem to be the most natural choice to carry out the forward-dynamics analysis of an acquired gait, but several options exist in their application. The paper explores such options for healthy and assisted gait, and concludes that the computed torque control of all the subject’s degrees of freedom is the alternative that provides the most accurate results. Moreover, the study of its more problematic underactuated variant accompanied by contact models showed to be connected to neighbor challenging topics as gait prediction or walking simulation of humanoids.

Damping Identification with Acceleration Measurements Based on Sensitivity Enhancement Method

The damping is important for forward and inverse structural dynamic analysis, and damping identification has become a hot issue in structural health monitoring recently. The dynamic responses of the structure can be measured in practice, and the structural parameter usually can be identified by inverse response sensitivity analysis. To reduce the measurement noise effect and enhance the effectiveness of the response sensitivity method, an enhanced sensitivity analysis method was proposed to identify the structural damping based on the Principal Component Analysis (PCA) method. The measured acceleration responses were analyzed by PCA method, and the updated analytical responses and the response sensitivities were projected into the subspace determined by the first‐order principal component. The projection equations were adopted to identify the parameters of damping model. The proposed damping identification method was numerically validated with a planar truss structure at first, and then the experimental study was conducted with a steel planar frame structure. It shows that the proposed method is effective in identifying the parameters of damping model with better accuracy compared with the conventional acceleration response sensitivity method, and it is also robust to the sensor placement and measurement noise.

Forward dynamic analysis of parallel robots using modified decoupled natural orthogonal complement method

This paper aims at the forward dynamic analysis of parallel robots by adding an effective modification on the Decoupled Natural Orthogonal Complement (DeNOC) method incorporating Virtual Spring Method (VSM). Forward dynamic analysis of parallel manipulators have been studied by many researches during the last decades, however, due to the complexity of closed-loop structures, it is still an attractive research subject in robotics. Developing VSM in energy based dynamic methods i.e., Lagrange formulation, has been demonstrated in literature before. In the current work, first, the VSM is briefly reviewed and its liaison with the Augmented Lagrange Method (ALM) is discussed. Next, among the Newtonian methods, the DeNOC which is based on the screw theory is elaborated. Then, inspired by the relation between VSM and ALM, the modified DeNOC (MDeNOC) is introduced. For more clarification, a 2DOF-five bar planar mechanism is chosen as case study and the aforementioned dynamic approaches are applied. Finally, the advantages and disadvantages of each method are illustrated. The key advantage of MDeNOC method is the ability of dynamic response and constraint reactions calculations with less preparation effort compared to DeNOC, while its accuracy is similar to Lagrange-VSM.

Limb position drift results from misalignment of proprioceptive and visual maps

Previous work (Brown et al., 2003a,b) has shown that limb position drifts when individuals make repetitive movements in the absence of visual feedback. The purpose of this study was to examine whether limb position drift might reflect a misalignment in visual and proprioceptive maps by examining the nature of information used to specify new movements from a drifted limb position. In a virtual reality (VR) environment, participants made continuous movements with their dominant right hand between two targets positioned 15cm apart, paced by a 0.625-Hz metronome. After 5 cycles, cursor feedback of the hand was removed for the next 44 cycles, which induced an average drift in hand position of roughly 5cm. On the 50th cycle, participants were required to move to one of 6 new targets from the drifted hand position. Kinematic analysis indicated that movement direction was unambiguously determined by the visual input marked by the original start position, or the last-seen hand position. Forward dynamics analysis revealed that current limb configuration was used to inform joint torques to produce this parallel direction. For new movement specification, accurate proprioceptive information about the drifted limb position was used, even though it was apparently not available for detecting drift in the first place. Movement distance varied directly with the extent of limb drift, although the differentiation of visual and proprioceptive control of distance could not be analyzed, as our control conditions were not significantly different for this measure. We suggest that movement drift, in the absence of visual feedback during cyclic repetitive movements, reflects a misalignment between largely accurate visual and proprioceptive maps, rather than a weighted fusion of the two modalities.

Influence of the controller design on the accuracy of a forward dynamic simulation of human gait

The analysis of a captured motion can be addressed by means of forward or inverse dynamics approaches. For this purpose, a 12 segment 2D model with 14 degrees of freedom is developed and both methods are implemented using multibody dynamics techniques. The inverse dynamic analysis uses the experimentally captured motion to calculate the joint torques produced by the musculoskeletal system during the movement. This information is then used as input data for a forward dynamic analysis without any control design. This approach is able to reach the desired pattern within half cycle. In order to achieve the simulation of the complete gait cycle two different control strategies are implemented to stabilize all degrees of freedom: a proportional derivative (PD) control and a computed torque control (CTC). The selection of the control parameters is presented in this work: a kinematic perturbation is used for tuning PD gains, and pole placement techniques are used in order to determine the CTC parameters. A performance evaluation of the two controllers is done in order to quantify the accuracy of the simulated motion and the control torques needed when using one or the other control approach to track a known human walking pattern.

A simple controller to overcome the lack of correlation between forward and inverse dynamic analysis of human motion tasks

The majority of biomechanical analyses of human motions, including those with musculoskeletal models, use inverse dynamic approaches due to its ability to deal with experimentally acquired kinematic and kinetic data. Yet, a forward dynamic approach can be more powerful and provide better insights on the transmission of forces in the internal biomechanical systems and structures of the human body. Although both approaches may use the same biomechanical model the results achieved do not necessarily correlate with each other. The aim of this study is to demonstrate the source of the lack of correlation between inverse and forward dynamics methodologies providing, in the process, insights on how to overcome such differences. Two types of problems involving the biomechanics of the spatial human motion are used to evaluate the correlation between the forward and inverse dynamic approaches: a gait analysis of a deterministic biomechanical model of the lower limbs, and, a full musculoskeletal model of the upper limb, which is characterised by the solution of a redundant muscle force sharing problem. For that purpose, an inverse dynamic model is applied to estimate the forces responsible for two experimentally acquired motions that are, afterwards, given as input to the forward dynamics model, which is used, in turn, to compute the kinematics of the biomechanical model. The comparison between the reference kinematics, acquired experimentally, and that resulting from the forward dynamic analysis supports that a lack of correlation between the inverse and forward dynamic analysis is always observed. It is proposed here, and demonstrated, that a controller implemented in a feedback loop is able to enhance numerical stability of the forward dynamics solution, leading to the ability of the forward dynamics approach to successfully simulate the acquired motions.

Interdependency of the maximum range of flexion–extension of hand metacarpophalangeal joints

Mobility of the fingers metacarpophalangeal (MCP) joints depends on the posture of the adjacent ones. Current Biomechanical hand models consider fixed ranges of movement at joints, regardless of the posture, thus allowing for non-realistic postures, generating wrong results in reach studies and forward dynamic analyses. This study provides data for more realistic hand models. The maximum voluntary extension (MVE) and flexion (MVF) of different combinations of MCP joints were measured covering their range of motion. Dependency of the MVF and MVE on the posture of the adjacent MCP joints was confirmed and mathematical models obtained through regression analyses (RMSE 7.7°).

A Biomechanical Model of the Scapulothoracic Joint to Accurately Capture Scapular Kinematics during Shoulder Movements.

The complexity of shoulder mechanics combined with the movement of skin relative to the scapula makes it difficult to measure shoulder kinematics with sufficient accuracy to distinguish between symptomatic and asymptomatic individuals. Multibody skeletal models can improve motion capture accuracy by reducing the space of possible joint movements, and models are used widely to improve measurement of lower limb kinematics. In this study, we developed a rigid-body model of a scapulothoracic joint to describe the kinematics of the scapula relative to the thorax. This model describes scapular kinematics with four degrees of freedom: 1) elevation and 2) abduction of the scapula on an ellipsoidal thoracic surface, 3) upward rotation of the scapula normal to the thoracic surface, and 4) internal rotation of the scapula to lift the medial border of the scapula off the surface of the thorax. The surface dimensions and joint axes can be customized to match an individual’s anthropometry. We compared the model to “gold standard” bone-pin kinematics collected during three shoulder tasks and found modeled scapular kinematics to be accurate to within 2mm root-mean-squared error for individual bone-pin markers across all markers and movement tasks. As an additional test, we added random and systematic noise to the bone-pin marker data and found that the model reduced kinematic variability due to noise by 65% compared to Euler angles computed without the model. Our scapulothoracic joint model can be used for inverse and forward dynamics analyses and to compute joint reaction loads. The computational performance of the scapulothoracic joint model is well suited for real-time applications; it is freely available for use with OpenSim 3.2, and is customizable and usable with other OpenSim models.

Substructural Condition Assessment Based on Force Identification and Interface Force Sensitivity

Time domain substructural condition assessment method is actively researched in recent years to avoid the problem with uncertainties in the different components of the structure, boundary conditions and with an improved effort in the inverse computation. Since the interface force between substructures would vary with the existence of local damages and excitation in the substructures, existing condition assessment method for a full structure cannot be applied directly to the substructures. Also, most existing approaches adopt the state space method in the response prediction. However, the state space method can be shown in this paper inaccurate in the forward substructural dynamic analysis due to the discretization error, and therefore identification based on this method cannot give satisfactory result for a substructure. The force identification for a full structure based on the explicit Newmark-β method has been shown superior to the state space method [K. Liu et al., J. Sound Vibr.33(3) (2014) 730–744]. This method is extended in this paper for substructural interface force identification. The variation of interface forces between substructures with variation in the substructural condition is illustrated with a plane truss structure. Subsequent condition assessment based on substructural response sensitivity is proposed with the analytical derivation of the sensitivity taking into account the interface force sensitivity which is not small to be ignored. The new damage detection method based on the explicit Newmark-β method and the substructural response sensitivity is verified numerically with different damage scenarios in a plane truss structure giving satisfactory results.