# Research on the Decoupling of the Parallel Vehicle Tilting and Steering Mechanism
## 2 Mechanism, Model, and Decoupling Method
### The Parallel Mechanism  
A spatial steering mechanism that is parallel to the tilting mechanism forms the tilting and steering parallel mechanism. The parallel mechanism is arranged symmetrically about the longitudinal symmetry plane of the vehicle (LSPV). The lengths of all of the symmetrically arranged components are correspondingly equal. The kingpins are set on both sides relative to the frame. As such, the points \(AB\), \(BO_{3}\), \(O_{3}O_{4}\), \(O_{4}A\), \(A^{\prime}B^{\prime}\), \(B^{\prime}O_{3}^{\prime}\), \(O_{3}^{\prime}O_{4}^{\prime}\), and \(O_{4}^{\prime}A^{\prime}\) (per Figure 1) are located on the same plane, which is called the tilt plane of the vehicle (TPV). The plane that is orthogonal to the TPV and containing \(O_{5}\)C is the LSPV. The plane \(\mathrm{P_{H}}\) is orthogonal to both the TPV and LSPV. The plane \(\mathrm{P_{H}}\) contains \(O_{5}\). The parallel mechanism is shown in Figure 1. The red part is the spatial steering mechanism; the green part is the tilting mechanism; the blue part is the wheels; and the black part is the frame (\(AA^{\prime}O_{4}^{\prime}O_{4}\)) and the other auxiliary lines. When the tilting mechanism drives the vehicle tilting to the left, the wheel on the left side moves up and the wheel on the right side moves down relative to the vehicle's coordinates. The opposite movement drives the vehicle to tilt to the right. In the tilting mechanism, the projections of the two kingpins \(HI\) and \(H^{\prime}I^{\prime}\) on the TPV are \(BO_{3}\) and \(B^{\prime}O_{3}^{\prime}\), respectively. \(HI\) is fixed to \(BO_{3}\) and \(H^{\prime}I^{\prime}\) is fixed to \(B^{\prime}O_{3}^{\prime}\). In order to make \(HI\) and \(H^{\prime}I^{\prime}\) translate relative to the frame \(AA^{\prime}O_{4}^{\prime}O_{4}\), the hinges \(AB\), \(BO_{3}\), \(O_{3}O_{4}\) and \(O_{4}A\) form a parallelogram and the hinges \(A^{\prime}B^{\prime}\), \(B^{\prime}O_{3}^{\prime}\), \(O_{3}^{\prime}O_{4}^{\prime}\) and \(O_{4}^{\prime}A^{\prime}\) form another parallelogram. These two parallelograms are arranged symmetrically around the LSPV. As such, the lengths of \(AB\), \(O_{3}O_{4}\), \(A^{\prime}B^{\prime}\) and \(O_{3}^{\prime}O_{4}^{\prime}\) are equal and the lengths of \(BO_{3}\), \(O_{4}A\), \(B^{\prime}O_{3}\) and \(O_{4}^{\prime}A^{\prime}\) are equal. The angle between \(BO_{3}\) (the projections of the lift kingpins \(HI\) on the TPV) and \(O_{5}\)C is the inclination angle (\(\varphi_{\mathrm{i}}\)) of the kingpin \(HI\). The angle between the projection of \(HI\) on the LSPV and \(O_{5}\)C is the caster angle (\(\varphi_{\mathrm{b}}\)) of the kingpin \(HI\). When the vehicle does not tilt, the angle between \(O_{1}O_{2}\) and \(\mathrm{P_{H}}\) is the camber angle (\(\varphi_{\mathrm{c}}\)) of the left wheel. When the vehicle does not turn, the angle between the projection of \(O_{1}O_{2}\) on  
Figure 1: Schematic diagram of the parallel mechanism. (**a**) The parallel mechanism without tilting and turning; (**b**) Projection of the parallel mechanism on the TPV when the vehicle tilts to the left and turns to the left; (**c**) Projection of the spatial steering mechanism on the \(\mathrm{P_{H}}\) when the vehicle tilts to the left and turns to the left. \(\mathrm{P_{H}}\) and \(\mathcal{O}_{4}\mathcal{O}_{5}\) is the toe angle (\(\varphi_{\mathrm{t}}\)) of the left wheel. Similarly, the inclination angle and the caster angle of the right kingpin \(H^{\prime}I^{\prime}\) can be realized and the camber angle and the toe angle of the right wheel can be realized. In the spatial steering mechanism, points \(O_{1}O_{2}\) and \(O_{2}G\) on the steering knuckle are fixed at \(O_{2}\). \(O_{1}O_{2}\) and \(O_{2}G\) rotate around _HI_. The angle between \(O_{1}O_{2}\) and \(O_{2}G\) is \(\varphi\). Similarly, \(O_{1}{}^{\prime}O_{2}{}^{\prime}\) and \(O_{2}{}^{\prime}G^{\prime}\) are fixed at \(O_{2}{}^{\prime}\). \(O_{1}{}^{\prime}O_{2}{}^{\prime}\) and \(O_{2}{}^{\prime}G^{\prime}\) rotate around \(H^{\prime}I^{\prime}\).