A Contact Force Solution for Non-Colliding Contact Dynamics Simulation

2006 ◽  
Author(s):  
Inna Sharf ◽  
Yuning Zhang
Keyword(s):  
Rigid Body ◽  
Contact Force ◽  
Contact Point ◽  
Closed Form Solution ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Friction Forces ◽  
Contact Points

Rigid-body impact modeling remains an intensive area of research spurred on by new applications in robotics, biomechanics, and more generally multibody systems. By contrast, the modeling of non-colliding contact dynamics has attracted significantly less attention. The existing approaches to solve non-colliding contact problems include compliant approaches in which the contact force between objects is defined explicitly as a function of local deformation, and complementarity formulations in which unilateral constraints are employed to compute contact interactions (impulses or forces) to enforce the impenetrability of the contacting objects. In this article, the authors develop a novel approach to solve the non-colliding contact problem for objects of arbitrary geometry in contact at multiple points. Similarly to the complementarity formulation, the solution is based on rigid-body dynamics and enforces contact kinematics constraints at the acceleration level. Differently, it leads to an explicit closed-form solution for the normal forces at the contact points. Integral to the proposed formulation is the treatment of tangential contact forces, in particular the static friction. These friction forces must be calculated as a function of microslip velocity or displacement at the contact point. Numerical results are presented for three test cases: 1) a thin rod sliding down a stationary wedge; 2) a cube rotating off the stationary wedge under application of an external moment and 3) the cube and the wedge both moving under application of a moment. To ascertain validity and correctness, the solutions to frictionless and frictional scenarios obtained with the proposed formulation are compared to those generated by using a commercial simulation tool MSC ADAMS.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

scholarly journals Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations

2009 ◽  
Vol 465 (2107) ◽  
pp. 2267-2292 ◽  
Author(s):  
Zhen Zhao ◽  
Caishan Liu ◽  
Bernard Brogliato
Keyword(s):  
Qualitative Analysis ◽  
Rigid Body ◽  
Numerical Simulations ◽  
Contact Point ◽  
Impulsive Differential Equations ◽  
Companion Paper ◽  
Rigid Body Dynamics ◽  
Drift Motion ◽  
Contact Points ◽  
Static Coefficient Of Friction

The objective of this paper is to implement and test the theory presented in a companion paper for the non-smooth dynamics exhibited in a bouncing dimer. Our approach revolves around the use of rigid body dynamics theory combined with constraint equations from the Coulomb's frictional law and the complementarity condition to identify the contact status of each contacting point. A set of impulsive differential equations based on Darboux–Keller shock dynamics is established that can deal with the complex behaviours involved in multiple collisions, such as the frictional effects, the local dissipation of energy at each contact point, and the dispersion of energy among various contact points. The paper will revisit the experimental phenomena found in Dorbolo et al . ( Dorbolo et al . 2005 Phys. Rev. Lett. 95 , 044101), and then present a qualitative analysis based on the theory proposed in part I. The value of the static coefficient of friction between the plate and the dimer is successfully estimated, and found to be responsible for the formation of the drift motion of the bouncing dimer. Plenty of numerical simulations are carried out, and precise agreements are obtained by the comparisons with the experimental results.

Wedge Damper Modeling and Forced Response Prediction of Frictionally Constrained Blades

2007 ◽  
Author(s):  
Ender Cigeroglu ◽  
Ning An ◽  
Chia-Hsiang Menq
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Harmonic Balance ◽  
Contact Stiffness ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Points ◽  
Contact Surfaces

In this paper, an improved wedge damper model is presented, based on which the effects of wedge dampers on the forced response of frictionally constrained blades are investigated. In the analysis, while the blade is modeled as a constrained structure, the damper is considered as an unconstrained structure. The model of the damper includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the damper is not artificially constrained. When modeling the contact surfaces of the wedge damper, discrete contact points along with contact stiffness are evenly distributed on the two contact surfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the engine rpm, quasi-static contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the centrifugal force. A friction model is employed to determine the three-dimensional nonlinear contact forces and the relationship between the contact forces and the relative motion is utilized by the Harmonic Balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations, in the Harmonic Balance method is in proportion to the number of modes employed, and therefore the number of contact points used is irrelevant. The developed method is applied to tuned bladed disk system and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that, the effect of rotational motion is significant, particularly for the in-phase vibration modes.

Influence of rail flexibility in a wheel/rail wear prediction model

2016 ◽  
Vol 231 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Javier F Aceituno ◽  
Pu Wang ◽  
Liang Wang ◽  
Ahmed A Shabana
Keyword(s):  
Prediction Model ◽  
Rigid Body ◽  
Contact Point ◽  
Three Dimensional ◽  
Contact Forces ◽  
Wear Model ◽  
Material Loss ◽  
Wear Prediction ◽  
Contact Points ◽  
Rail Wear

The aim of this paper is to study the influence of rail flexibility when a wheel/rail wear prediction model that computes the material loss based on an energy approach is used. The wheel/rail wear model used in this investigation is a simplified combined wear hypothesis that is based on the frictional energy loss in the contact patch. In order to account for wear and its distribution in a profiled wheel surface, the contact forces, creepages and location of the wheel/rail contact points are first calculated using a fully nonlinear multibody system (MBS) and three-dimensional contact formulations that account for the rail flexibility. The contact forces, creepages and contact point locations are defined as nonlinear functions of the rail deformations. These nonlinear expressions are used in the wear calculations. The wear distribution is considered to be proportional to the normal force in the contact area. Numerical simulations are first performed in order to compare between the results obtained using the simplified wheel/rail wear model and the results obtained using Archard’s wear model with a focus on sliding when the track is modeled as a rigid body. This simplified wear model is then used in the simulation of the MBS vehicle model in the case of a flexible body track, in which the rails are modeled using the finite element floating frame of reference approach and modal reduction techniques. The effect of the rail deformation on the wear results are examined by comparing these results with those obtained using the rigid-body track model.

A 2D Bristle Friction Force Model for Contact Dynamics Simulation

2009 ◽  
Author(s):  
Ou Ma ◽  
Jianxun Liang ◽  
Steven Fillmore
Keyword(s):  
Contact Point ◽  
Friction Model ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Contact Friction ◽  
Force Model ◽  
Tangential Plane ◽  
Friction Forces ◽  
Body Contact ◽  
Frictional Behavior

This paper describes a 2D bristle contact friction model which is capable of modeling and simulating frictional behavior in both sliding and sticking regimes occurring in general 3D rigid-body contact. The model extends the 1D integrated bristle friction model to a 2D space by allowing the “bristle spring” to not only stretch along the direction of the relative velocity but also rotate due to the direction change of the velocity or motion trend in the common tangential plane of the contacting surfaces involved at the contact point of interest. With such an extension, the resulting friction model can be readily used to compute 3D contact friction forces in both sticking and sliding regimes for a general 3D contact dynamics model working with a multibody dynamics simulation application. Several simulation examples are provided to demonstrate the effectiveness of the model for predicting the experimentally seen frictional behavior such as sticking, stickslip, and sliding.

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
Normal Vector ◽  
Optimization Criteria ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

scholarly journals Electromyography-Driven Forward Dynamics Simulation to Estimate In Vivo Joint Contact Forces During Normal, Smooth, and Bouncy Gaits

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Swithin S. Razu ◽  
Trent M. Guess
Keyword(s):  
Contact Force ◽  
Temporal Patterns ◽  
Musculoskeletal Model ◽  
Contact Forces ◽  
Dynamics Simulation ◽  
Muscle Forces ◽  
Model Predictions ◽  
Subject Specific ◽  
Full Body

Computational models that predict in vivo joint loading and muscle forces can potentially enhance and augment our knowledge of both typical and pathological gaits. To adopt such models into clinical applications, studies validating modeling predictions are essential. This study created a full-body musculoskeletal model using data from the “Sixth Grand Challenge Competition to Predict in vivo Knee Loads.” This model incorporates subject-specific geometries of the right leg in order to concurrently predict knee contact forces, ligament forces, muscle forces, and ground contact forces. The objectives of this paper are twofold: (1) to describe an electromyography (EMG)-driven modeling methodology to predict knee contact forces and (2) to validate model predictions by evaluating the model predictions against known values for a patient with an instrumented total knee replacement (TKR) for three distinctly different gait styles (normal, smooth, and bouncy gaits). The model integrates a subject-specific knee model onto a previously validated generic full-body musculoskeletal model. The combined model included six degrees-of-freedom (6DOF) patellofemoral and tibiofemoral joints, ligament forces, and deformable contact forces with viscous damping. The foot/shoe/floor interactions were modeled by incorporating shoe geometries to the feet. Contact between shoe segments and the floor surface was used to constrain the shoe segments. A novel EMG-driven feedforward with feedback trim motor control strategy was used to concurrently estimate muscle forces and knee contact forces from standard motion capture data collected on the individual subject. The predicted medial, lateral, and total tibiofemoral forces represented the overall measured magnitude and temporal patterns with good root-mean-squared errors (RMSEs) and Pearson's correlation (p2). The model accuracy was high: medial, lateral, and total tibiofemoral contact force RMSEs = 0.15, 0.14, 0.21 body weight (BW), and (0.92 < p2 < 0.96) for normal gait; RMSEs = 0.18 BW, 0.21 BW, 0.29 BW, and (0.81 < p2 < 0.93) for smooth gait; and RMSEs = 0.21 BW, 0.22 BW, 0.33 BW, and (0.86 < p2 < 0.95) for bouncy gait, respectively. Overall, the model captured the general shape, magnitude, and temporal patterns of the contact force profiles accurately. Potential applications of this proposed model include predictive biomechanics simulations, design of TKR components, soft tissue balancing, and surgical simulation.

Analysis and Visualization of the Contact Force Solution Space for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Solution Process ◽  
Solution Space ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components ◽  
The Relationship

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them for simplifying the solution process, and then the static equilibrium equations are applied to find certain contact force components and the relationship between the others. Using the friction cone equation at each foot contact point and the known contact force components, the problem is transformed into a geometrical one to find the ranges of contact forces and the relationship between them that satisfy the friction constraint. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the whole solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Optimal Contact Force Distribution for Multi-Limbed Robots

2005 ◽  
Vol 128 (3) ◽  
pp. 566-573 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
New Strategy ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The incremental strategy of opening up the friction cones is aided by using the “force space graph” which indicates where the solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Rigid Body dynamics and decoupled control architecture for two strongly interacting manipulators

Robotica ◽  
1991 ◽  
Vol 9 (4) ◽  
pp. 421-430 ◽  
Author(s):  
M.A. Unseren
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Equations Of Motion ◽  
Joint Space ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Control Architecture ◽  
Reduced Order ◽  
Closed Chain

SUMMARYA rigid body dynamical model and control architecture are developed for the closed chain motion of two structurally dissimilar manipulators holding a rigid object in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the generalized contact forces. The problem of solving the joint space and reduced order models for the unknown variables is discussed. A new control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the force and position-controlled degrees of freedom during motion of the system. The proposed composite controller enables the designer to develop independent, non-interacting control laws for the force and position control of the complex closed chain system.

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