Marek Wojtyra

Multibody Simulation Model of Human Walking

Abstract A three-dimensional simulational model of a human walking is presented. The biped is anthropomorphic, i.e., its inertial and kinematical properties are similar to human ones. The biped consists of eight rigid bodies. Each leg consists of three parts: thigh, shank, and foot. The trunk is modeled as two rigid bodies connected by a revolute joint. The inertia properties of head and arms are included in trunk properties. Each leg has 7 degrees of freedom. The whole modelled biped has 21 degrees of freedom. The impact and friction effects are considered in the ground reaction force modeling. The ground is represented by a flat, rigid surface. The normal to the ground component of reaction force depends on penetration of the foot into the ground and on the velocity of this penetration. The tangential reaction is represented in terms of a pseudo-Coulomb friction model (in this model of friction there is no stiction phase, i.e., the bodies are moving relative to each other at a negligibly small velocity). The direction of friction force depends on the relative movement velocity; the magnitude depends on the friction coefficient, the normal force magnitude, and also (nonlinearly) on the relative velocity. The direct dynamic problem is solved. Human gait patterns, derived from measurements of human walking, are used to calculate the necessary driving torques. A simple closed-loop control algorithm for stabilizing the motion is applied. The control system of the biped is not engaged in the planning of the trajectory; this task is realized following the gait pattern. The main task of the control system is to modify slightly and instantaneously the prescribed gait to prevent the biped from losing stability. To account for the elasticity of human tissues, so-called wobbling masses are introduced to the model. Both rigid body and wobbling mass models are validated by comparing obtained results of simulations with measurements of human walking. Advantages and disadvantages of the direct dynamics approach to human walking analysis are discussed.

Properties of the Dahl Model Applied to Modelling of Static Friction in Closed-Loop Kinematic Chains

High parametric sensitivity of the Dahl model is observed when rigid body approach is used to analyse the static friction in close-loop mechanisms. The origins of sensitivity problems are investigated. The possibility of diminishing sensitivity problems by taking flexibility into account is discussed.

Application of General Multibody Methods to Robotics

In this chapter robotic applications of general multibody system (MBS) simulation methods, based on absolute coordinates formalism, are presented. Three typical problems, often encountered in robotics, are discussed: kinematic analysis with singular configuration detection, simulation of parallel robot dynamics investigated jointly with the robot control systems properties, and finally, simulation of a robot with flexibility effects taken into account. In case of singular configuration detection simplest types of singular configurations are analyzed – turning point and bifurcation point. The second case of MBS application is an example of parallel robot dynamic analysis when model based control is taken into account. The last part of the chapter is devoted to the analysis of complex, flexible power transmission mechanism carried out with general MBS formalism.

Stewart platform based parallel manipulator destined for the kinematic's justification of two cooperated robots

The paper presents a virtual prototype of a new design of parallel manipulator of Stewart Platform type destined for the measuring applications. The concept of the 6 DOF manipulator is described. The model of mechanical part of the robot is built in UNIGRAPHICS system and ADAMS/spl trade/ environment. Preliminary results of simulations and initial investigations concerned with measuring applications, and conclusions are presented. Main advantages of this solution are simplicity, compactness and lightness of the construction. The POLMAN design provides a systematic approach to the development of modular parallel robotic systems which can be configured into a wide variety of different forms for different applications.

Comparison of Dynamic Properties of Two KUKA Lightweight Robots

This paper concerns the comparison of dynamic properties of two LWR 4+ robots. As a preparation to the identification task, a series of joint torque measurements is performed to determine the variability of the dynamic parameters. The torque measurements from two robots are compared with each other and a simplified multibody model. The results are discussed.

Modeling of Static Friction in Closed-Loop Kinematic Chains with Multiple Degrees of Freedom—A Study of Uniqueness and Parametric Sensitivity Problems

Problems with uniqueness and high parametric sensitivity of solution of equations of motion, encountered in the static friction regime, are addressed. Friction in joints of a multiple degree of freedom closed-loop kinematic chains is discussed. Two different models of friction are studied: the discontinuous Coulomb model with stiction regime represented in terms of additional constraints and the approximate Coulomb model, smoothed in the vicinity of zero relative velocity. Origins of non-uniqueness and high sensitivity are investigated; the questionable credibility of the stiction regime simulation results is pointed out. Two examples are provided to illustrate the discussed issues.

Numerical Detection of Inactive Joints

Inactive joints are the joints that cannot perform relative motion due to structural limitations in a mechanism. They are usually introduced in order to eliminate redundant constraints. A joint can be inactive in the whole range of the mechanism motion or only in selected configurations. A numerical method of detection of inactive joints is presented. The method is based on multibody system approach and utilizes the constraint Jacobian matrix. The ability to perform relative motion is investigated and inactivity of joints in both regular and singular configurations is discussed. A numerical example is provided.

On Some Problems With Modeling of Coulomb Friction in Self-Locking Speed Reducers

A simple mathematical model of friction in speed reducers is presented and discussed. A rigid body approach, typical for multibody simulations, is adopted. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms.The first version of the model is purely rigid, i.e. no deflections of the mechanism bodies are allowed. Constraints are introduced to maintain the ratio between input and output velocity. It is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, coefficient of friction and inertial parameters) two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints and Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Examples of all indicated paradoxical situations are provided and discussed.The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input-output velocity ratio are introduced). In non-paradoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previously paradoxical situations no multiple solutions of friction force are found, however, the amended model does not solve all problems. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. Numerical examples showing behavior of the model are provided and analyzed.Copyright

Multibody Modelling of a Tracked Robot’s Actuation System

A simulation model of a mobile robot is presented in the chapter. The robot is equipped with four track systems, wrapped around four movable and independently driven track holders. Driving torques are transmitted to the track systems and track holders via speed reducers. The study is focused on friction effects in gearing, and especially on the self-locking properties. A simplified mathematical model of friction in speed reducers is presented. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms. This friction model is implemented in a general purpose simulation software in which the entire tracked mobile robot is modelled. A multibody model of the complete robot is briefly described. Simulation results obtained for different friction levels, varying from friction absence to friction beyond the self-locking limit, are compared and discussed. The robot motors are also modelled and requirements for electric power in various operating conditions are estimated.

A Comparison of Various Methods of Redundant Constraints Handling in Multibody System Simulations

When redundant constraints are present in a rigid body mechanism, only selected joint reactions can be determined uniquely, whereas the other cannot. Analytic criteria and numerical methods of finding joints with uniquely solvable reactions are available. In this paper the problem of joint reactions solvability is examined from the point of view of numerical methods frequently used for redundant constrains handling in practical simulations. Three methods are discussed: elimination of redundant constraints, pseudoinverse-based calculations and the augmented Lagrangian method. In each method the redundant constraints are treated differently which — in case of joints with non-unique reactions — leads to different reaction solutions. Moreover, it is shown that one and the same method may lead to different solutions, provided that input data are prepared differently. Finally, it is illustrated that — in case of joints with solvable reactions — the obtained solutions are unique, regardless of the method used for redundant constraints handling.Copyright