RSSR Mechanism Design and Motion Control Strategy of a Carbon-Free Vehicle for Obstacle Avoidance Competition

Abstract

With the popularity of carbon-free vehicle obstacle avoidance races, the requirements for the accuracy and reliability of vehicle motion control are getting higher and higher. Aiming at the problems of trajectory deviation and debugging difficulties of the carbon-free vehicle during the movement process, the Revolute-Slider-Slider-Revolute (RSSR) mechanism is adopted as the steering device, which is aimed at improving the motion control precision and obstacle avoidance ability of the vehicle. Firstly, from the kinematics point of view, a kinematics model based on the spatial four-link mechanism is established, and the influence of each parameter change on the trajectory of the vehicle is analyzed. On this basis, the influence of each key parameter on the motion process is further explored through practical debugging, so as to derive a general law of the vehicle’s motion under the drive of the RSSR mechanism. Through numerical simulation analysis, the accuracy of the theoretical model is verified, and the structural design of the vehicle is optimized accordingly. The actual debugging results show that the vehicle can realize smooth operation, which fully proves the practicality and effectiveness of the established mathematical model and the research of the RSSR mechanism.

1. Introduction

A carbon-free vehicle is a mechanical device powered by gravitational potential energy that converts this natural force into kinetic energy for self-propulsion. This ingenious device relies solely on gravitational potential energy and does not require any external energy source; it follows a predetermined trajectory through precise mechanical design, while skillfully performing directional control and obstacle avoidance. Since 2009, the Department of Higher Education of the Ministry of Education has organized several sessions of the National Comprehensive Competence Competition for College Students in Engineering Training with the theme of “carbon-free vehicle”, aiming to deepen the reform of teaching and cultivate the comprehensive competence of college students in engineering practice and at the same time advocate a low-carbon and environmentally friendly lifestyle [1,2,3].

The design of the carbon-free vehicle in the competition environment strictly prohibits the use of any electronic sensors or intelligent detection technologies to recognize obstacles. The layout of obstacles on the track follows established rules and is pre-set, and the trajectories of the vehicle, including S-shapes, 8-shapes and double 8-shapes, are designed to achieve effective avoidance of these obstacles. In order to accurately follow these pre-set trajectories, the vehicle must be carefully mechanically designed and meticulously tuned to ensure that it can follow the designed paths accurately to successfully avoid the obstacles and complete the competition. According to the specifications of the S-shaped obstacle avoidance competition, the participating three-wheeled carbon-free vehicles are required to utilize their limited gravitational potential energy to skillfully avoid equally spaced cylindrical obstacles spaced at 1 m intervals on a set course. The performance of the vehicle is scored based on the number of obstacles successfully avoided as it successfully navigates around the predetermined S-shaped track.

The vehicle needs to have precise motion control and efficient energy utilization to achieve optimal obstacle avoidance and completion of the trajectory [4,5]. The design of the carbon-free vehicle involves many aspects, including structural design, kinematic analysis, trajectory control, etc., of which the most critical is how to realize efficient energy conversion and precise motion control. At present, scholars have proposed a variety of design schemes and conducted relevant theoretical studies. For example, Wang et al. designed an S-type carbon-free vehicle with a “crank rocker” as the steering mechanism and carried out kinematic simulation and analysis using ADAMS software [6]. Ai et al. investigated a steering control scheme based on a crank–slider mechanism [7]. Han et al. summarized the tracing principle of a double 8-word track carbon-free vehicle and designed a carbon-free vehicle using a crank rocker mechanism and an incomplete gear steering mechanism [8,9]. In addition, some scholars have proposed a steering system design based on a “cam mechanism” and simulated and optimized the travel trajectory of the vehicle [10,11,12]. Despite the progress of existing research, the trajectory control and parameter adjustment of carbon-free vehicles still face challenges in practical applications. For example, factors such as machining and assembly errors and environmental disturbances may affect the trajectory of the vehicle. In order to solve these problems, Hu et al. designed and simulated the wheel layout of a single-wheel-drive carbon-free vehicle using ADAMS software [13], Tian et al. improved the accuracy of trajectory control by innovatively designing the fine-tuning mechanism of the carbon-free vehicle [14] and Chen et al. designed a fine-tuning device with high adjustment accuracy by introducing a worm gear mechanism and a micrometer that was for later correction of trajectory errors [15]. Chen et al. proposed an evaluation method for trajectory overlap and established an optimization model for the running trajectory of the vehicle [16]. Gong et al. proposed a steering scheme for a positive RSSR mechanism that reduces the cost while simplifying the mechanical structure and improving the transmission efficiency [17].

Based on previous studies, we improved the structural design of the S-shaped track carbon-free vehicle for the layout of the S-shaped track and the specific distribution of obstacles and utilized the RSSR mechanism to achieve the periodic steering of the vehicle as a way to reach the obstacle avoidance goal. In addition, a fine-tuning scheme is designed for the RSSR steering mechanism to improve the flexibility and accuracy of the system. In the paper, we first describe the design scheme of the vehicle in detail. By constructing a mathematical model of the traveling motion of the vehicle, we studied the motion characteristics of the vehicle and analyzed in detail the influence of the change in the rod length parameter on the motion trajectory in the RSSR mechanism. Combined with the actual fabrication and testing experience, we summarized a set of general debugging methods for the vehicle.

2. Design Proposal

The vehicle is mainly composed of the following key parts: steering and adjustment mechanism, frame, transmission system and traveling mechanism. The core motion principle is as follows, when the weight falls, its gravitational potential energy is transformed into the rotational power of the extended range pulley and this process further drives the rotation of the spool of the vehicle. At both ends of the spool, the crank and large gear are fixed, respectively, so that the rotary motion of the spool can be effectively transmitted. Specifically, the rotational motion of the spool is transmitted to the front fork through the designed RSSR mechanism, which enables the front fork to execute periodic oscillation to realize the steering function of the vehicle. At the same time, the power of the spool is also transmitted to the driving wheel through a one-stage gear meshing system, providing the vehicle with forward momentum. This design not only ensures the flexibility of the motion of the vehicle but also improves its motion efficiency and control accuracy. The sketch of the motion of the vehicle is shown in Figure 1 and the physical drawing is shown in Figure 2.

The steering and adjustment part is the core component of the vehicle. In order to simplify the mechanical structure, reduce the interference of part inertia on the motion of the vehicle and enhance the smoothness of the drive system, a spatial RSSR mechanism consisting of articulated bearings at both ends is used. In order to eliminate the mechanism’s sharp return characteristic, the center axes of the crank and rocker were kept at the same horizontal height. In addition, in order to correct errors that may occur during the manufacturing and installation process and to ensure the adjustability of the trajectory of the vehicle movement, a variety of adjusting devices are introduced, which not only improve the flexibility and adaptability of the vehicle but also provide the possibility of precise adjustment of the trajectory. The specific structure of the RSSR steering and adjusting devices is demonstrated in Figure 3.

The design of the crank has been improved by changing it from the traditional long rod shape to a disk shape machined with Archimedes spiral grooves. This design permits fine adjustment by simply adjusting the position of the retaining bolt in the helix groove. In order to realize the adjustment of the length of the con-rod, articulating bearings are used at both ends and are connected by means of a screw with positive and negative fine threads. The length of the con-rod can be easily adjusted by changing the number of turns by which the screw is screwed in or out.

In addition, a V-shaped fine-tune structure is designed in order to adjust the deflection angle of the front wheel in a small range. Its working principle is shown in Figure 4. In the initial state, it is assumed that the con-rod is free to stretch. When the adjustment lever B is moved from position 1 to position 2, it appears that the con-rod is stretched. However, in reality, since the con-rod is a rigid body, it will not be elongated; therefore, the lever A will rotate around the center point of rotation O by a tiny angle $\gamma$, thus realizing the fine adjustment of the front wheel deflection angle. In order to facilitate the observation and recording of the front wheel swing angle, an angle disk is introduced. By means of the scale value on the angle disk, the debugging of the vehicle can be completed quickly, which also ensures the accuracy and repeatability of the debugging process.

To ensure the accuracy of the vehicle’s trajectory and to avoid installation errors introduced by multiple disassembly, an integrally designed body was adopted, which was realized through selective laser sintering (SLS) printing technology [18,19]. The body is manufactured using nylon material, which not only helps to reduce the overall weight of the vehicle but also enhances durability. A simple and highly efficient one-stage gear system was selected to improve the system’s energy utilization.

3. Mathematical Model

The mathematical relationship of the vehicle’s obstacle avoidance motion can be represented by the block diagram shown in Figure 5.

3.1. Motion Analysis of the RSSR Mechanism

The RSSR mechanism selected for the steering device is a positive space four-bar mechanism consisting of the first and last two rotating pairs and the middle two ball–hinge pairs [20,21]. In order to find the output angle $\beta$ of the rocker $L_3$ as a function of the input angle $\theta$ of the crank $L_1$, a space right-angled coordinate system is established, as shown in Figure 6, and the spatial coordinates of the points B and C are derived:

$$\left(\begin{array}{l}{x}_B\hfill \\ y_B\hfill \\ z_B\hfill \end{array}\right)=\left(\begin{array}{c}{x}_0\\ 0\\ 0\end{array}\right)+\left[J_{AB}\right]\left(\begin{array}{l}0\hfill \\ 0\hfill \\ L_1\hfill \end{array}\right)=\left(\begin{array}{c}{x}_0\\ L_1\sin \theta \\ L_1\cos \theta \end{array}\right)$$

(1)

$$\left(\begin{array}{l}{x}_C\hfill \\ y_C\hfill \\ z_C\hfill \end{array}\right)=\left(\begin{array}{c}0\\ y_0\\ 0\end{array}\right)+\left[J_{CD}\right]\left(\begin{array}{c}{L}_2\\ L_3\\ 0\end{array}\right)=\left(\begin{array}{c}{L}_3\cos \beta \\ y_0+L_3\sin \beta \\ 0\end{array}\right)$$

(2)

Points B and C are always constrained by the con-rod BC during their motion [10], and their rod length constraint equations are:

$${\left(x_B-x_C\right)}^2+{\left(y_B-y_C\right)}^2+{\left(z_B-z_C\right)}^2={L_2}^2$$

(3)

Substituting Equations (1) and (2) into Equation (3) and expanding them leads to the equation:

$$W\sin \beta +F\sin \beta +Q=0$$

(4)

where $W={\displaystyle \frac{y_0}{\left|AB\right|}}-\cos \theta$, $F=-{\displaystyle \frac{y_0}{\left|AB\right|}}$, $Q={\displaystyle \frac{{y_0}^2+{x_0}^2+|AB{|}^2+|CD{|}^2-\left|BC\right|}{2\left|AB\right|\left|CD\right|}}-{\displaystyle \frac{x_0\cos \theta +x_0\sin \theta }{\left|CD\right|}}$.

• Then, it can be solved:

  $$\beta =2\arctan \left({\displaystyle \frac{W\pm \sqrt{W^2+F^2-Q^2}}{F-Q}}\right)$$

  (5)

3.2. Motion Analysis of the Vehicle

When the weight falls from a very small height $\mathrm{d}h$, the vehicle will travel a very small displacement $\mathrm{d}s$, at which point the resulting geometric relationship is shown in Figure 7:

$$\mathrm{d}s=\mathrm{d}h{r}_1/i{r}_2$$

(6)

where $r_1$ is rear wheel radius and $r_2$ is spool radius. The radius of curvature of the trajectory at the center point of the rear axle is:

$$\rho ={\displaystyle \frac{b_1}{\tan \beta }}-{\displaystyle \frac{b_2}{2}}$$

(7)

The point $O^{\prime }$ in Figure 7 is the center of curvature of the trajectory and also the instantaneous center of velocity of the vehicle’s motion, so the absolute displacement of the outer wheel of the vehicle is:

$$\mathrm{d}{s}^{\prime }={\displaystyle \frac{\rho +b_2}{\rho }}\mathrm{d}s$$

(8)

bringing Equation (8) to $\mathrm{d}\alpha =\mathrm{d}s/\rho$ and integrating yields:

$$\alpha ={\displaystyle \frac{r_1}{i{r}_2}}{\displaystyle {\int }_0^h\left(\frac{\tan \beta }{b_1-b_2\tan \beta }\right)}\mathrm{d}h$$

(9)

The equations of motion for both wheels and the front wheel can be obtained by integration as:

$$\begin{array}{l}\left\{\begin{array}{c}x=-{\displaystyle \frac{r_1}{i{r}_2}}{\displaystyle {\int }_0^h\sin }\alpha \mathrm{d}h\\ y={\displaystyle \frac{r_1}{i{r}_2}}{\displaystyle {\int }_0^h\cos }\alpha \mathrm{d}h\end{array}\right.\\ \left\{\begin{array}{l}{x}_l=x+b_2\cos \alpha \hfill \\ y_l=y+b_2\sin \alpha \hfill \end{array}\right.\\ \left\{\begin{array}{l}{x}_r=x+b_2\cos \alpha -b_1\sin \alpha \hfill \\ y_r=y+b_2\sin \alpha +b_1\cos \alpha \hfill \end{array}\right.\end{array}$$

(10)

where $x_l$ and $y_l$ represent the position of the left wheel and $x_r$ and $y_r$ represent the position of the right wheel.

Equation (10) is the mathematical expression for the motion of the vehicle.

4. Numerical Simulation and Analysis of Results

4.1. Kinematic Analysis

The functional relationship (Equation (5)) of the RSSR mechanism is written into the corresponding computer statements [22,23], and the data in

Table 1. Structural parameters.

Name	Gear Center Distance	Captain of Vehicle	Width of Vehicle	Gear Ratio	Rear Wheel Radius	Length of Crank	Length of Con-Rod	Length of Rocker
symbolic	d1 [mm]	b1 [mm]	b2 [mm]	i	r1 [mm]	L1 [mm]	L2 [mm]	L3 [mm]
value	30	120	110	6	65	21	70	39

of the structural parameters can be assigned to each parameter to obtain the graph of the swing angle $\beta$ of the rocker as a function of the crank angle $\theta$, as shown in Figure 8.

Under the premise of considering the existence of the crank, the parameters of the crank, con-rod and rocker were gradually adjusted in the simulation based on the data in

Table 2. Comparison parameters.

Index	Length of Crank [mm]	Length of Con-Rod [mm]	Length of Rocker [mm]
1	20.3	68.6	38.3
2	20.4	68.8	38.4
3	20.5	69.0	38.5
…	…	…	…
12	21.5	72.8	39.5

. By carefully observing the effects of these parameter changes on the curve shape, the following conclusions are drawn:

• When the lengths of the con-rod and rocker are kept constant, an increase or decrease in the crank length will directly affect the amplitude of the curve but has no effect on the periodicity of the curve change. This indicates that the crank length is the key factor that affects the amplitude of the motion without affecting the periodicity of the motion.
• With the crank and rocker lengths fixed, changing the length of the con-rod will cause the curve to translate in the direction of the longitudinal axis. This change does not affect the amplitude of the curve or its periodicity, indicating that the length of the con-rod mainly affects the starting position of the motion without changing the basic characteristics of the motion.
• Changing only the length of the rocker, we find that the effect is the same as when the length of the crank is changed. This further confirms that the crank and the rocker have similar roles in affecting the motion profile and that together they determine the magnitude of the profile.

These findings are helpful in understanding and optimizing the motion characteristics of the vehicle. A comparison of the variation of the corner curves is detailed in Figure 9, which visualizes the effect of different parameter adjustments on the kinematic trajectory.

In order to deeply investigate the specific effect of the variation of each rod length on the running trajectory of the vehicle, the equations of the motion of the vehicle (10) were first transformed into executable codes. Using these codes and based on the data in Table 1 of the structural parameters, simulation experiments were conducted to obtain a typical cosine-like trajectory, as shown in Figure 10. This initial simulation result provided us with a baseline trajectory for subsequent parameter variation analysis.

Subsequently, the lengths of the crank and con-rod were gradually adjusted and the simulation was re-run based on the data presented in Table 2. By measuring and comparing the simulation results with the trajectory change trends shown in Figure 11, the following conclusions were drawn:

• Effect of crank length: when keeping the length of the con-rod and rocker constant, increasing or decreasing the crank length will result in a corresponding increase or decrease in the period of the trajectory curve. At the same time, this change will also cause the vehicle motion to deviate to one side, thus affecting the overall motion path of the vehicle.
• Effect of con-rod length: while keeping the crank and rocker lengths constant, changing the length of the con-rod will cause the car body to be deflected. However, this deflection has less effect on the cyclic variation of the trajectory curve. This implies that the adjustment of the con-rod length mainly affects the symmetry of the vehicle’s motion rather than its underlying motion period.

These findings help to understand how to optimize the motion trajectory of the vehicle by adjusting the rod length parameter. The motion characteristics of the vehicle can be more precisely controlled by careful parameter adjustment.

4.2. Physical Test Analysis

To further verify the accuracy of the simulation analysis, the carbon-free vehicle was physically tested. In the experiment, the vehicle was placed in the starting position and the weight was lifted to the maximum height before each test. According to the data in Table 2, only one rod length size was adjusted each time and several starting tests were conducted. By repeatedly observing and comparing the movement of the vehicle, the following patterns were found:

• Influence of the crank: the length of the crank directly affects the maximum curvature of the traveling trajectory of the vehicle. When the crank length increases, the left and right deflection angle of the front wheels of the vehicle will increase accordingly, which is manifested in the motion trajectory as the compression of the cycle and the deflection of the vehicle body.
• The role of the con-rod: the con-rod is the key component for adjusting the front wheel deflection angle distribution. It can adjust the size of the left and right deflection angles individually without changing the sum of the left and right deflection angles of the front wheels. This is reflected in the trajectory, as the motion cycle remains unchanged but the vehicle body is deflected. To ensure that the direction of operation of the vehicle is not deflected, the length of the con-rod needs to be precisely fine-tuned.
• Commissioning of the RSSR mechanism vehicle: for the vehicle with the RSSR mechanism, the crank length should be adjusted first to adapt the period of the running trajectory to the spacing of the obstacles when the key dimensions such as the diameter of the rear wheels, the transmission ratio, the length of the vehicle and the width of the vehicle have already been determined during the commissioning. Then, the con-rod length should be adjusted to correct the vehicle deflection. Alternatively, the V fine-tune structure can be used to directly adjust the left and right deflection angles of the front wheels by changing the size of the V tension angle until the vehicle movement is no longer deflected.

5. Conclusions

This article comprehensively analyzes the existing literature and discusses the design methodology, motion simulation, trajectory control and its optimization strategy for a carbon-free vehicle. Firstly, the design background and competition requirements of carbon-free vehicles are reviewed and the main contents of related research are elaborated. Then, the design scheme of the vehicle with an RSSR mechanism as the steering device is proposed and the fine-tuning scheme of the crank, con-rod and front wheel deflection is introduced, a complete mathematical model is established and the specific influence of the change in the four-rod parameter on the motion trajectory of the vehicle is explored in depth through the simulation analysis and then the design parameters are optimized. Combined with the actual debugging, the rationality of the fine-tuning scheme and the accuracy of the mathematical model and simulation results of the vehicle are further verified, and the general method of vehicle debugging is summarized.

For a carbon-free vehicle, its mass, length, width and the size of its wheels are important factors that affect its actual trajectory. These parameters are not only related to the stability and motion accuracy of the vehicle but also directly associated with its obstacle avoidance ability and energy utilization efficiency. The summarized commissioning method is carried out on the basis that these parameters have been determined to ensure that the vehicle can achieve the expected performance in practical applications. However, there is still room for optimization between parameters such as the structure and size of the vehicle and the efficient use of energy. Therefore, future research could further explore how these parameters can be adjusted to improve the efficiency of the vehicle’s energy utilization while maintaining its stability and obstacle avoidance capabilities.