# Analysis, Design, and Experimental Research of a Novel Wheelchair-Stretcher Assistive Robot
## 2 Mechanical Structure Design of the Wheelchair-Stretcher Assistive Robot
### Kinematics, Dynamics Analysis and Optimization of the Folding Mechanism  
#### 2.2.1 Kinematics Analysis and Parameters Optimization of the Folding Mechanism  
Folding mechanism is the key to realizing the safe and smooth switching between wheelchair and stretcher. Analyzing the movement characteristic of the wheelchair-stretcher assistive robot and researching the references [23; 24; 25; 26; 27], the corresponding mechanism is proposed, as shown in Figure 7.  
There is one rack, five motion components and seven revolute joints in the mechanism. On the basis of the computing formula of the degree of freedom for the planar linkage mechanism [28], the following equation can be obtained:  
\[dof=3n-2P_{L}-P_{H}=1 \tag{6}\]  
where \(n\) is the number of motion components, \(P_{L}\) is the number of lower pair, and \(P_{H}\) is the number of higher pair. Parallelogram structure composed by the calf support plate, foot pedal, connecting rod and the seat plate has no effect on the motion of the whole folding mechanism. Therefore, the motion of the quadrilateral structure, which consisted of the seat plate, side link 1, armrests and side link 2, is only analyzed. In order to determine the structural size of the mechanism, the minimum conclusive area, which is the smallest plane region produced in a period for the motion of the folding mechanism, is used as the optimization function [29]. The movement diagram of the whole mechanism is shown in Figure 8.  
Figure 6: The mechanical structure design of the Mecanum wheel; 1—case cover of the walking wheel, 2—bear, 3—shaft of the Mecanum wheel, 4—connecting plate of the Mecanum wheel, 5—connecting plate of the walking wheel, 6—the Mecanum wheel, 7—HTD5 driven belt pulley, 8—the upper cover of the bearing block, 9—the lower cover of the bearing block. Figure 7: Schematic diagram of folding mechanism; 1—the seat plate, 2—side link 1, 3—armrests, 4—side link 2, 5—caff support plate, 6—connecting rod, 7—foot pedal. The two positions shown in Figure 8 are the limit positions of the movement of the planar linkage, and the region formed by the two limit positions is the smallest region of the planar linkage and can be described as:  
\[S=S_{1}+S_{2}+S_{3}+S_{4}. \tag{7}\]  
In this formula, area \(S_{1}\) of \(\Delta ADC\) is given as,  
\[S_{1}=\sqrt{p(p-l_{4})\cdot(p-l_{3})\cdot(p-l_{2})} \tag{8}\]  
where \(l_{2}=290\) mm is the length of side link 1. The optimal parameter \(l_{3}\) is the length of the armrests. The optimal parameter \(l_{4}\) is the length of side link 2. And \(p=\frac{l_{3}+l_{4}+AC}{2}\). Area \(S_{2}\) of \(\Delta ABC\) is expressed as,  
\[S_{2}=\frac{1}{2}l_{1}\cdot l_{2}\cdot\sin\angle ABC \tag{9}\]  
where \(l_{1}=555\) mm is the length of the seat plate. Area \(S_{3}\) of sector \(CBC_{1}\) is written as:  
\[S_{3}=\frac{1}{4}\pi l_{2}^{2}. \tag{10}\]  
Area \(S_{4}\) of trapezoid \(ABC_{1}D_{1}\) is described as:  
\[S_{4}=\frac{(l_{1}+l_{2})\cdot|AB|_{y}}{2}. \tag{11}\]  
In the meantime, the relationship expressions between \(l_{3},l_{4}\) and \(\alpha,\beta\) can be determined as follows,  
\[ \begin{array}{l}l_{4}\cdot\sin\beta+l_{3}\cos\alpha=l_{1}\cos(\angle D_{1}AB ),\\ l_{4}\cdot\cos\beta-l_{3}\sin\alpha=l_{1}\sin(\angle D_{1}AB)+l_{2}\end{array}  \tag{12}\]  
where \(\alpha\) is the angle between the armrests link and the horizontal direction. \(\beta\) is the angle between the side link 2 and the vertical direction. \(\angle D_{1}AB\) is the angle between the side link 2 in the limit position and the seat plate. Simplifying Equation (12), the following equations can be derived:  
\[ \begin{array}{l}l_{3}=\frac{l_{1}\cos(\angle D_{1}AB)\cos\beta-l_{1}\sin( \angle D_{1}AB)\sin\beta-l_{2}\sin\beta}{(\sin\alpha\sin\beta+\cos\alpha\cos \beta)},\\ l_{4}=\frac{l_{1}\sin\alpha\cos(\angle D_{1}AB)+l_{1}\cos\alpha\sin\beta+\cos \alpha\cos\beta}{\sin\alpha\sin\beta+\cos\alpha\cos\beta}.\end{array}  \tag{13}\]  
Figure 8: Schematic diagram of the planar four-bar linkage.