# The State of the Art of Biomechanics Applied in Ergonomic Furniture Design
## 3 Findings and Discussions
### Biomechanical Analysis and Testing Methods
#### 3.2.1 Mechanical Models  
At present, most research on human movement biomechanics is based on the establishment of simplified mathematical-mechanical models, or the establishment of complex multibody dynamics models, including multiple parts of the human skeleton and muscle [73; 74]. What to include in a model depends on the intended use of the model [75]. The simplest biomechanical motion models typically reduce the human body to a mass and do not take into account its own rotation and deformation. For example, the simplest model used to study walking is the inverted pendulum [76]. For complex motions, mathematical models are simplified compared to the real body, but they generate a formidable number of equations [77]. According to GB/T 17245 [78]; a regression equation can be established to predict the body segment mass and center of mass, expressed as Equation (1):  
\[Y=B_{0}+B_{1}X_{1}+B_{2}X_{2} \tag{1}\]  
where \(Y\) is the body segment mass \(m\) (unit: kg) or body segment center of the mass position \(mc\) (unit: mm), and the body segment center of the mass position \(mc\) is the distance from the starting point of the center of the mass measurement to the center of mass of the body segment; \(X_{1}\) is the body weight, unit: kg; \(X_{2}\) is the body height, unit: mm; \(B_{0}\) is the constant term of the regression equation; \(B_{1}\) is the regression coefficient of the body weight; and \(B_{2}\) is the regression coefficient of the body height.  
GB/T 17245 specifies the coefficients of the binary regression equation coefficients for calculating the body segment mass, the center of the mass position, and the overall center of the mass position of the human body based on body weight and height. A model for calculating the center of the mass position of the human body based on the mass of the body segments can be established. According to theoretical mechanics, if the object consists of several parts, and its \(i\)-th part mass is \(\text{m}_{i}\) and the center of mass is \((x_{i},y_{i},z_{i})\), the center of mass of the object \((x_{c},y_{c},z_{c})\) is shown in Equation (2):  
\[\begin{cases}x_{c}=\frac{\sum_{i=1}^{n}m_{i}x_{i}}{\sum_{i-1}^{n}m_{i}}\\ y_{c}=\frac{\sum_{i=1}^{n}m_{i}y_{i}}{\sum_{i-1}^{n}m_{i}}\\ z_{c}=\frac{\sum_{i=1}^{n}m_{i}}{\sum_{i}^{n}}\end{cases} \tag{2}\]  
According to Equation (2), the equation for calculating the center of mass of the human body based on the geometric model of the body center of mass calculation can be expressed as Equation (3):  
\[x_{c}=\frac{\sum_{i=1}^{n}m_{i}x_{i}}{\sum_{i-1}^{n}m_{i}},\;y_{c}=\frac{\sum_ {i=1}^{n}m_{i}y_{i}}{\sum_{i-1}^{n}m_{i}},\;z_{c}=\frac{\sum_{i=1}^{n}m_{i}z_{ i}}{\sum_{i-1}^{n}m_{i}} \tag{3}\]  
where \(n\) is the number of human body segments divided by Equation (3). The human body mass center coordinates can be obtained.  
The model of the human center of mass provides a basic description of the principles governing human movement, enabling us to comprehend the trajectory, velocity, acceleration, and other factors associated with motion [73]. Human motion biomechanics problems are more analyzed by a multi-rigid body model. According to the actual needs, a multirigid body model can be a simple local joint model or a complex whole body model [79]. As shown in Figure 5[75,80], a more complete model for human motion simulation should include: (1) a skeleton model; (2) a muscle path model; (3) a musculotendon actuation model; (4) a muscle excitation-contraction coupling model; and (5) a motor task goal model.