# Improving techniques for center of mass estimation using statically equivalent serial chain modeling

## Date of Award

2013

## Degree Name

M.S. in Mechanical Engineering

## Department

Department of Mechanical and Aerospace Engineering

## Advisor/Chair

Advisor: Andrew P. Murray

## Abstract

Any system composed of rigid bodies connected by revolute, spherical, and/or universal joints defines a Statically Equivalent Serial Chain (SESC). The SESC is a virtual serial chain that terminates at the center of mass (CoM) of the original system. The SESC is defined by the individual link masses, the CoM location of each mass, the distance between the joints, and the relative joint axis orientations. The joint angles of the SESC change corresponding to the movement of the original system, thereby keeping its terminus pointing at the CoM location of the original system for any configuration. A SESC may be generated experimentally without any knowledge of the individual link masses, the CoM location of each mass, and the distance between the joints. The data that is needed includes the relative orientations between joint axes, the current joint values, and the CoM of the entire articulated system. In most cases, the SESC can be derived with only partial CoM information collected for each configuration. An example of this is collecting the x and y values of the CoM in a horizontal plane while not knowing its height or z value. The resulting SESC is able to generate the location of the CoM for an arbitrary configuration given the joint angles. Necessary conditions are generated on the minimum number of data points needed to generate a SESC. The minimum number needed depends on the number of links of the original system, the dimension of the CoM data collected for each configuration, and a measure of the degree of redundancy in the columns of the matrix associated with the initial SESC modeling.This thesis presents four developments toward recognizing the SESC as a practical modeling technique. First, modifications to a matrix necessary in computing the SESC model are proposed. The modifications are required due to redundant columns that arise in the matrix as part of the modelling process. Second, a SESC is developed via experimentation for a spatial articulated rigid-body system. The SESC was derived from planar CoM data and joint readings, and generated predictions of the spatial CoM with acceptable accuracy. Third, problems of generating a SESC experimentally are presented and a possible remedy is proposed. If only partial dimensions of the CoM are measured during data collecting, and the CoM locations of one or more bodies in the system cannot be changed with respect to the unmeasured direction, then the SESC derived experimentally cannot predict the system's CoM location in the unmeasured direction. A potential remedy for this problem is that the stationary body has a similar mass distribution (identical or symmetric) to a second body in the system, and both bodies are the outer most links in their branches. For this case, the SESC modeling for the full CoM estimation would not be impacted. This observation is particularly useful in studies including human or humanoid subjects, because these subjects are likely to keep one foot on the ground when they keep static balance and the two feet are (roughly) symmetric bodies. Fourth, with the goal of understanding the quantity of data required before the experimentally-constructed SESC obtains acceptable accuracy, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. A general form of the function for estimating the error of the experimental SESC is proposed

## Keywords

Center of mass Mathematical models, Kinematics Mathematical models, Mechanical engineering; Statically Equivalent Serial Chain; center of mass; SESC

## Rights Statement

Copyright © 2013, author

## Recommended Citation

Li, Bingjue, "Improving techniques for center of mass estimation using statically equivalent serial chain modeling" (2013). *Graduate Theses and Dissertations*. 611.

https://ecommons.udayton.edu/graduate_theses/611