Conditions for dynamic balance of a rigid body with heavy foot

Milos Zivanovic,Mihailo Lazarevic

doi:10.5937/fmet1501055z

Abstract

The model of a rigid body and heavy foot joined by the revolute joint in the constant gravitational field is described. The rigid body moves in the vertical plane, whereas the heavy foot lies on the flat, very rough horizontal support. Conditions for the dynamic balance of this system are mathematically expressed by using the ZMP method. It is shown that they determine an area in the phase space in which the state of the system should be in order that its dynamic balance is kept. It is also shown by appropriate simulations of motion of the system in the dynamic balance that these conditions are not sufficient for the system to keep its upright posture, but are in connection with its controllability. It is briefly discussed what are the necessary conditions for this system in dynamic balance to keep its upright posture.

Highlights

We consider a rigid body of the mass m joined by the revolute joint to the foot of the mass mf
In the dynamic balance the foot is at rest, and the center of pressure P coincides with the zero moment point, which is placed in the support segment
The mathematical model of a rigid body with heavy foot is given, and the conditions for the system to be in dynamic balance are mathematically defined

Summary

INTRODUCTION

We consider a rigid body of the mass m joined by the revolute joint to the foot of the mass mf. As long as the system posture is dynamically balanced, the foot will be at rest, while the rigid body will rotate around the axis z that is immobile with respect to the supp ort. In this case, among all projectio ns of the torque M , only the projection Mz = M k to the axis z affects the rotation of the rigid body. M y are balanced with corresponding projections of torques of the rigid body weight, and static and dynamic reactions [3] in revolute joint, with respect to the point A.

C C cos sin

CONDITIONS FOR DYNAMIC BALANCE OF THE SYSTEM

SIMULATION OF MOTION OF THE SYSTEM IN DYNAMIC BALANCE

DYNAMIC BALANCE AND UPRIGHT POSTURE OF THE SYSTEM

CONCLUSION