Equations based on simple anthropometric measurements to predict body fat percentage (BF%) are lacking in Chinese population with increasing prevalence of obesity and related abnormalities. We aimed to develop and validate BF% equations in two independent population-based samples of Chinese men and women. The equations were developed among 960 Chinese Hans living in Shanghai (age 46·2 (sd 5·3) years; 36·7 % male) using a stepwise linear regression and were subsequently validated in 1150 Shanghai residents (58·7 (sd 6·0) years; 41·7 % male; 99 % Chinese Hans, 1 % Chinese minorities). The associations of equation-derived BF% with changes of 6-year cardiometabolic outcomes and incident type 2 diabetes (T2D) were evaluated in a sub-cohort of 780 Chinese, compared with BF% measured by dual-energy X-ray absorptiometry (DXA; BF%-DXA). Sex-specific equations were established with age, BMI and waist circumference as independent variables. The BF% calculated using new sex-specific equations (BF%-CSS) were in reasonable agreement with BF%-DXA (mean difference: 0·08 (2 sd 6·64) %, P= 0·606 in men; 0·45 (2 sd 6·88) %, P< 0·001 in women). In multivariate-adjusted models, the BF%-CSS and BF%-DXA showed comparable associations with 6-year changes in TAG, HDL-cholesterol, diastolic blood pressure, C-reactive protein and uric acid (P for comparisons ≥ 0·05). Meanwhile, the BF%-CSS and BF%-DXA had comparable areas under the receiver operating characteristic curves for associations with incident T2D (men P= 0·327; women P= 0·159). The BF% equations might be used as surrogates for DXA to estimate BF% among adult Chinese. More studies are needed to evaluate the application of our equations in different populations.

This paper presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form.

The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be modelled. The output of the package is high-level computer program code for evaluation of various kinematic and dynamic variables: the homogeneous transformation matrix between the hand and base coordinate frame, Jacobian matrices, driving torques and the elements of dynamic model matrices. The dynamic model is based on the recursive Newton-Euler equations. The application of recursive symbolic relations yields nearly minimal numerical complexity. Further improvement of computational efficiency is achieved by introducing different computational rates for the terms depending on joint angles, velocities and accelerations. A comparative study of numerical complexity for several typical industrial robots is presented.