An Efficient Manipulator Dynamics Formulation Based Upon Newton-Euler Equations and the ZRP Method

1992 ◽  
Author(s):  
Harry Hui Cheng ◽  
Krishna C. Gupta
Keyword(s):  
Euler Equations ◽  
Inverse Dynamics ◽  
Robot Manipulator ◽  
End Effector ◽  
Reference Position ◽  
Joint Reaction Forces ◽  
Position Data ◽  
Angular Velocities ◽  
Reaction Forces ◽  
Zero Reference

Abstract This paper presents a formulation of robot manipulator inverse dynamics based upon the Newton-Euler equations and the zero reference position method. The angular velocities and accelerations, linear accelerations of the mass centers, and inertia forces and moments of each link of the manipulator are computed recursively starting from the base to the end-effector. But, the joint reaction forces and moments, and joint actuator forces or torques are computed recursively from the end-effector to the base. The formulation is at first carried out in the current position and then reformulated by directly utilizing the zero reference position data. The former formulation is intuitively simple; while the latter is computationally more efficient. A parametric study is also conducted to compare the relative efficiency of this formulation with the previously available formulation.

Adding flexibility to the links of a rigid-link dynamic model of an articulated robot

Robotica ◽  
1989 ◽  
Vol 7 (2) ◽  
pp. 165-168 ◽  
Author(s):  
A. Bodner
Keyword(s):  
Computational Complexity ◽  
Dynamic Model ◽  
Euler Equations ◽  
Inverse Dynamics ◽  
Small Degree ◽  
End Effector ◽  
Rigid Link ◽  
Link Model ◽  
Articulated Robot ◽  
Special Case

SUMMARYA method was developed that takes into account flexibility of robot links in the inverse dynamics calculations. This method uses the Newton-Euler equations and is applicable for special case systems that allow for only a small degree of flexibility. Application of the method should improve the accuracy of the position of the end effector during motion of the robot.The results of this study show that the method can be based entirely on an existing rigid-link model with only minimal changes required as additions. The computational complexity of the method is discussed briefly as well and indicates an increase of computations of slightly more than a factor of two as compared to a rigid-link model for the same robot geometry.

Influence of the Musculotendon Dynamics on the Muscle Force-Sharing Problem of the Shoulder—A Fully Inverse Dynamics Approach

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Quental Carlos ◽  
Azevedo Margarida ◽  
Ambrósio Jorge ◽  
Gonçalves S. B. ◽  
Folgado João
Keyword(s):  
Muscle Activation ◽  
Inverse Dynamics ◽  
Glenohumeral Joint ◽  
Inverse Dynamic ◽  
Force Sharing ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Muscle Activations ◽  
Joint Reaction

Abstract Most dynamic simulations are based on inverse dynamics, being the time-dependent physiological nature of the muscle properties rarely considered due to numerical challenges. Since the influence of muscle physiology on the consistency of inverse dynamics simulations remains unclear, the purpose of the present study is to evaluate the computational efficiency and biological validity of four musculotendon models that differ in the simulation of the muscle activation and contraction dynamics. Inverse dynamic analyses are performed using a spatial musculoskeletal model of the upper limb. The muscle force-sharing problem is solved for five repetitions of unloaded and loaded motions of shoulder abduction and shoulder flexion. The performance of the musculotendon models is evaluated by comparing muscle activation predictions with electromyography (EMG) signals, measured synchronously with motion for 11 muscles, and the glenohumeral joint reaction forces estimated numerically with those measured in vivo. The results show similar muscle activations for all muscle models. Overall, high cross-correlations are computed between muscle activations and the EMG signals measured for all movements analyzed, which provides confidence in the results. The glenohumeral joint reaction forces estimated compare well with those measured in vivo, but the influence of the muscle dynamics is found to be negligible. In conclusion, for slow-speed, standard movements of the upper limb, as those studied here, the activation and musculotendon contraction dynamics can be neglected in inverse dynamic analyses without compromising the prediction of muscle and joint reaction forces.

Generalized Constraint and Joint Reaction Forces in the Inverse Dynamics of Spatial Flexible Mechanical Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 777-784 ◽  
Author(s):  
D. C. Chen ◽  
A. A. Shabana ◽  
J. Rismantab-Sany
Keyword(s):  
Inverse Dynamics ◽  
Mechanical Systems ◽  
Flexible Body ◽  
Body Dynamics ◽  
Joint Reaction Forces ◽  
Flexible Body Dynamics ◽  
Reaction Forces ◽  
Applied Forces ◽  
Generalized Constraint ◽  
Joint Reaction

In both the augmented and recursive formulations of the dynamic equations of flexible mechanical systems, the inerita, constraints, and applied forces must be properly defined. The inverse dynamics is a commonly used approach for the force analysis of mechanical systems. In this approach, the system is kinematically driven using specified motion trajectories, and the objective is to determine the driving forces and torques. In flexible body dynamics, however, a force that acts at a point on the deformable body is equipollent to a system, defined at another point, that consists of the same force, a moment that depends on the relative deformation between the two points, and a set of generalized forces associated with the elastic coordinates. Furthermore, a moment in flexible body dynamics is no longer a free vector. It is defined by the location of its line of action as well as its magnitude and direction. The joint reaction and generalized constraint forces represent equipollent systems of forces. Both systems in flexible body dynamics are function of the deformation. In this investigation, a procedure is developed for the determination of the joint reaction forces in spatial flexible mechanical systems. The mathematical formulation of some mechanical joints that are often encountered in the analysis of constrained flexible mechanical systems is discussed. Expressions for the generalized reaction forces in terms of the constraint Jacobian matrices of the joints are presented. The effect of the elastic deformation on the reaction forces is also examined numerically using the spatial flexible multibody RSSR mechanism that consists of a set of interconnected rigid and elastic bodies. The procedure described in this investigation can also be used to determine the joint torques and actuator forces in kinematically driven spatial elastic mechanism and manipulator systems.

Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design

2019 ◽  
Vol 2 (2) ◽  
pp. 2
Author(s):  
Denis Mosconi ◽  
Adriano Almeida Gonçalves Siqueira ◽  
Everthon Silva Fonseca
Keyword(s):  
Feedback Loop ◽  
Inverse Dynamics ◽  
Robot Manipulator ◽  
Linear Quadratic Regulator ◽  
Robotic Systems ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
End Effector ◽  
The Right

To ensure the correct positioning of the end-effector of robot manipulators is one of the most important objectives of the robotic systems control. Lack of reliability in tracking the reference trajectory, as well as in the desired final positioning compromises the quality of the task to be performed, even causing accidents. The purpose of this work was to propose an optimal controller with an inner loop based on the dynamic model of the manipulator and a feedback loop based on the Linear Quadratic Regulator, in order to ensure that the end effector is in the right place, at the right time. The controller was compared to the conventional PID, presenting better performance, both in the transient response, eliminating overshoot, and steady-state, eliminating the stationary error.

Adaptation of the AnyBody™ Musculoskeletal Shoulder Model to the Nonconforming Total Shoulder Arthroplasty Context

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Lauranne Sins ◽  
Patrice Tétreault ◽  
Nicola Hagemeister ◽  
Natalia Nuño
Keyword(s):  
Contact Area ◽  
Shoulder Arthroplasty ◽  
Humeral Head ◽  
Inverse Dynamics ◽  
Center Of Pressure ◽  
Total Shoulder Arthroplasty ◽  
Strong Support ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Joint Reaction

Current musculoskeletal inverse dynamics shoulder models have two limitations to use in the context of nonconforming total shoulder arthroplasty (NC-TSA). First, the ball and socket glenohumeral (GH) joint simplification avoids any humeral head translations. Second, there is no contact at the GH joint to compute the contact area and the center of pressure (COP) between the two components of NC-TSA. In this paper, we adapted the AnyBody™ shoulder model by introducing humeral head translations and contact between the two components of an NC-TSA. Abduction in the scapular plane was considered. The main objective of this study was to adapt the AnyBody™ shoulder model to a NC-TSA context and to compare the results of our model (translations, COP, contact area, GH joint reaction forces (GH-JRFs), and muscular forces) with previous numerical, experimental, and clinical studies. Humeral head translations and contact were successfully introduced in our adapted shoulder model with strong support for our findings by previous studies.

Quantifying Force Magnitude and Loading Rate from Drop Landings That Induce Osteogenesis

2001 ◽  
Vol 17 (2) ◽  
pp. 142-152 ◽  
Author(s):  
Jeremy J. Bauer ◽  
Robyn K. Fuchs ◽  
Gerald A. Smith ◽  
Christine M. Snow
Keyword(s):  
Hip Joint ◽  
Inverse Dynamics ◽  
Initial Contact ◽  
Ground Reaction Forces ◽  
Loading Rates ◽  
Impact Peak ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Drop Landings ◽  
Joint Reaction

Drop landings increase hip bone mass in children. However, force characteristics from these landings have not been studied. We evaluated ground and hip joint reaction forces, average loading rates, and changes across multiple trials from drop landings associated with osteogenesis in children. Thirteen prepubescent children who had previously participated in a bone loading program volunteered for testing. They performed 100 drop landings onto a force plate. Ground reaction forces (GRF) and two-dimensional kinematic data were recorded. Hip joint reaction forces were calculated using inverse dynamics. Maximum GRF were 8.5 ± 2.2 body weight (BW). At initial contact, GRF were 5.6 ± 1.4 BW while hip joint reactions were 4.7 ± 1.4 BW. Average loading rates for GRF were 472 ± 168 BW/s. Ground reaction forces did not change significantly across trials for the group. However, 5 individuals showed changes in max GRF across trials. Our data indicate that GRF are attenuated 19% to the hip at the first impact peak and 49% at the second impact peak. Given the skeletal response from the drop landing protocol and our analysis of the associated force magnitudes and average loading rates, we now have a data point on the response surface for future study of various combinations of force, rate, and number of load repetitions for increasing bone in children.

scholarly journals Criteria of Motion Without Slipping for an Omnidirectional Mobile Robot

2021 ◽  
Vol 17 (4) ◽  
pp. 527-546
Author(s):  
I. S. Mamaev ◽  
◽  
A. A. Kilin ◽  
Yu. L. Karavaev ◽  
V. A. Shestakov ◽  
...  
Keyword(s):  
Mobile Robot ◽  
Euler Equations ◽  
Elementary Geometry ◽  
Supporting Surface ◽  
Dynamical Equations ◽  
Omnidirectional Mobile Robot ◽  
Angular Velocities ◽  
Reaction Forces ◽  
Position And Orientation ◽  
Omnidirectional Wheels

In this paper we present a study of the dynamics of a mobile robot with omnidirectional wheels taking into account the reaction forces acting from the plane. The dynamical equations are obtained in the form of Newton – Euler equations. In the course of the study, we formulate structural restrictions on the position and orientation of the omnidirectional wheels and their rollers taking into account the possibility of implementing the omnidirectional motion. We obtain the dependence of reaction forces acting on the wheel from the supporting surface on the parameters defining the trajectory of motion: linear and angular velocities and accelerations, and the curvature of the trajectory of motion. A striking feature of the system considered is that the results obtained can be formulated in terms of elementary geometry.

Dynamic Analysis of Geared Robotic Mechanisms Using Graph Theory

1996 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Dar-Zen Chen ◽  
Ta-Wei Lin
Keyword(s):  
Dynamic Analysis ◽  
Transmission Lines ◽  
Inverse Dynamics ◽  
Robot Manipulator ◽  
Open Loop ◽  
Graph Representation ◽  
Mechanical Transmission ◽  
Tree Structures ◽  
Reaction Forces ◽  
Two Degree Of Freedom

Abstract A systematic methodology is developed for the dynamic analysis of a class of geared robotic mechanisms. The concepts of canonical graph representation, the equivalent open-loop chain, and the mechanical transmission lines of a mechanism are used to organize the analysis. The approach modifies the Newton-Euler recursive inverse dynamics algorithm for open-loop chains and tree structures to include gear joints. A recursive method for the evaluation of reaction forces is developed. It is shown that reaction forces can be efficiently computed from the highest level primary links followed by the secondary links, one or two levels at a time, working toward the base. This procedure is especially useful when the evaluation of dynamic loads of bearings and teeth teeth is desired for the design of such mechanisms. A two degree-of-freedom robot manipulator is used as an illustrative example.

Knee Joint Loading During Lineman-Specific Movements in American Football Players

2015 ◽  
Vol 31 (3) ◽  
pp. 142-148 ◽  
Author(s):  
Rebecca L. Lambach ◽  
Jay W. Young ◽  
David C. Flanigan ◽  
Robert A. Siston ◽  
Ajit M.W. Chaudhari
Keyword(s):  
Inverse Dynamics ◽  
Cartilage Damage ◽  
American Football ◽  
3 Dimensional ◽  
Increase Risk ◽  
Joint Reaction Forces ◽  
Cartilage Injuries ◽  
Univariate Anova ◽  
Reaction Forces ◽  
Joint Reaction

Linemen are at high risk for knee cartilage injuries and osteoarthritis. High-intensity movements from squatting positions (eg, 3-point stance) may produce high joint loads, increasing the risk for cartilage damage. We hypothesized that knee moments and joint reaction forces during lineman-specific activities would be greater than during walking or jogging. Data were collected using standard motion analysis techniques. Fifteen NCAA linemen (mean ± SD: height = 1.86 ± 0.07 m, mass = 121.45 ± 12.78 kg) walked, jogged, and performed 3 unloaded lineman-specific blocking movements from a 3-point stance. External 3-dimensional knee moments and joint reaction forces were calculated using inverse dynamics equations. MANOVA with subsequent univariate ANOVA and post hoc Tukey comparisons were used to determine differences in peak kinetic variables and the flexion angles at which they occurred. All peak moments and joint reaction forces were significantly higher during jogging than during all blocking drills (all P < .001). Peak moments occurred at average knee flexion angles > 70° during blocking versus < 44° in walking or jogging. The magnitude of moments and joint reaction forces when initiating movement from a 3-point stance do not appear to increase risk for cartilage damage, but the high flexion angles at which they occur may increase risk on the posterior femoral condyles.

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