A stiffness matrix method for foot force distribution of walking vehicles

1992 ◽  
Vol 22 (5) ◽  
pp. 1131-1138 ◽  
Author(s):  
X. Gao ◽  
S.-M. Song
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Force Distribution ◽  
Foot Force

A Generalized Stiffness Matrix Method for Force Distribution of Robotic Systems with Indeterminancy

1993 ◽  
Vol 115 (3) ◽  
pp. 585-591 ◽  
Author(s):  
Xiaochun Gao ◽  
Shin-Min Song ◽  
Chun Qi Zheng
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Robotic Systems ◽  
Force Distribution ◽  
Force Analysis ◽  
Chain Geometry ◽  
Walking Machines ◽  
Foot Force ◽  
Closed Chain ◽  
Finger Forces

Foot forces in walking machines and finger forces in multi-fingered grippers are usually indeterminate due to the multi-closed-chain geometry of the systems. While many methods were proposed to solve the force distribution of such systems, a method called stiffness matrix method [2] was developed based on the concept that the force must satisfy the equations of material deformations. However, only leg compliances were considered in the stiffness matrix method. In this paper, the stiffness matrix method is generalized to include all the major system compliances, i.e., those of legs (fingers), actuators and terrain (object to be grasped). Based on the developed generalized stiffness matrix method, an example of foot force analysis of a quadruped is presented to demonstrate the effects of different system compliances on the foot forces.

Foot force distribution of walking machine with consideration of terrain properties

1992 ◽  
Vol 29 (4-5) ◽  
pp. 497-514 ◽  
Author(s):  
Chun Qi Zheng ◽  
Shin-Min Song ◽  
G.E.O. Widera
Keyword(s):  
Force Distribution ◽  
Walking Machine ◽  
Foot Force

The stiffness matrix method

Structures ◽  
2000 ◽  
pp. 239-285
Author(s):  
M. S. Williams ◽  
J. D. Todd
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method

Body Vibrations of a Legged Walking Machine

1992 ◽  
Author(s):  
Xiaochun Gao ◽  
Shin-Min Song
Keyword(s):  
The Body ◽  
Robotic Systems ◽  
Force Distribution ◽  
Walking Machine ◽  
Foot Force ◽  
Robot Hands ◽  
Machine Systems ◽  
External Loads ◽  
Wheeled Vehicles ◽  
Quadrupedal Walking

Abstract Unlike in wheeled vehicles, compliance in walking machine systems changes due to the variation of leg geometry, as its body proceeds. This variation in compliance will cause vibration, even if external loads remain constant. A theory is thus developed to predict the body vibrations of a walking machine during walking. On the other hand, dynamic foot forces under body vibrations can be computed by application of the existing numerical methods. As an example, the body vibrations of a quadrupedal walking chair under different walking conditions are simulated in terms of the developed theory. The results show that the influence of body vibrations on the foot force distribution is essential and, in some cases, the walking chair may lose its stability due to its body vibrations, even though it is identified to be stable in a quasi-static analysis. The developed theory can also be extended to other similar multi-limbed robotic systems, such as multi-fingered robot hands.

Static Elastic-Plastic Analysis of a Pipe Structure by the Transfer Matrix Method

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Masayuki Arai ◽  
Shoichi Kuroda ◽  
Kiyohiro Ito
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Frame Structure ◽  
Pipe System ◽  
Curved Pipe ◽  
Elastic Plastic ◽  
Complex Problems ◽  
Element Method

Abstract Pipe systems have been widely used in industrial plants such as power stations. In these systems, the displacement and stress distributions often need to be predicted. Analytical and numerical methods, such as the finite element method (FEM), boundary element method (BEM), and frame structure method (FSM), are typically adopted to predict these distributions. The analytical methods, which can only be applied to problems with simple geometries and boundary conditions, are based on the Timoshenko beam theory. Both FEM and BEM can be applied to more complex problems, although this usually requires a stiffness matrix with a large number of degrees-of-freedom. In FSM, although the structure is modeled by a beam element, the stiffness matrix still becomes large; furthermore, the matrix size needed in FEM and BEM is also large. In this study, the transfer matrix method, which is simply referred to as TMM, is studied to effectively solve complex problems, such as a pipe structure under a small size stiffness matrix. The fundamental formula is extended to a static elastic-plastic problem. The efficiency and simplicity of this method in solving a space-curved pipe system that involves an elbow are demonstrated. The results are compared with those obtained by FEM to verify the performance of the method.

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