Kinematic chain study of the adjustability of a monolateral external fixator

Abstract

Adjustability of the external fixator reflects two important features–the range of allowable locations of pins and the ease of frame application. In this study, multilink open chain kinematic equations were developed to examine this adjustability of a monolateral external fixator. The entire bone‐fixator system was simulated by a manipulator with four rigid links, two spherical joints, and one prismatic joint. Each of the links and joints was described by a 4×4 homogenous transformational matrix with either X‐Y‐Z or Z‐X‐Z Euler angle representation. The transformation equations were developed by concatenating these transformational matrices. Then the kinematic equations were solved by the least squares optimization method, and the numerical solutions were validated by geometrical solutions and mechanical experiments. The results showed solutions using Z‐X‐Z Euler angle representations were more reliable in predicting the reducibility of the malalignment and could be more conveniently used for direct kinematic study. Increasing the length of the central body, the offset of the telescoping joint, and the rotational range of ball joints and decreasing the pin length increased the adjustability. The adjustability reached its maximum as the initial offset of the telescoping joint reached a critical level. In conclusion, the adjustability of the external fixators was closely related to their designs. This study may assist manufacturers in the design of external fixators and help surgeons better understand the restraints of fixators and hence use such equipment more effectively.