Design and Prototype a Stair-Climbing Wheelchair

The Centers for Disease Control and Prevention announced in 2023 that 12.1% of U.S. adults have a mobility disability causing serious difficulty walking or climbing stairs [1]. In general, approximately 10% of the U.S. population has some type of physical disability or mobile impairment that necessitates the use of wheelchairs or other mobility devices for their daily locomotion [2]. However, the effectiveness of wheelchairs is limited as they are unable to surmount obstacles such as stairs. Those individuals are constantly searching for alternative routes to avoid stairs that cannot be traversed safely without external aids. Installing ramps, wheelchair lifts, and residential stairlifts are possible solutions, but they are relatively costly and are often only temporary necessities for patients [3]. A few examples as shown in Fig. 1, require the disabled to enhance their houses with extra devices that allow them to enter and travel to different floors.

Although mounting extra facilities seems to be a solution for low-rise buildings, adding all these devices to make their homes accessible can quickly become very costly, as opposed to the cost of one universal wheelchair that could travel up any set of stairs along with standard sidewalks. Moreover, providing such facilities for all exits on every floor of a high-rise building, for instance, is almost impossible. In recent decades, researchers have been trying to come up with solutions for a wheelchair to negotiate the stairs, but their designs were rather bulky, expensive, unfeasible, or impossible and sometimes needed additional assistance other than the patient to operate the machine [4–8].

A common solution or design choice for stair-climbing vehicles is the use of track transmission systems as used in heavy machinery such as dozers or tanks [9–11]; they provide a great deal of traction and stability during stair-climbing operations but sacrifice the ride comfort for the patient. This kind of transmission system also consumes a lot of energy while being heavy and cumbersome. In addition, tracks may damage the pavement or stairs since their main purpose is to generate good traction in muddy and rough terrains as well as struggling to traverse efficiently on flat ground. This design application can be seen in the Genesis Mobile Stairlift [12] where the wheelchair is designed specifically for stair-climbing operations and strays away from straight translation.

While combining the benefits of tracks for stair-climbing operation and the efficiency of wheels on ground translation, some designs take the approach of a hybrid locomotion system between tracks and wheels, as seen in the power wheelchair Scewo BRO [13]. Although a hybrid locomotion system may successfully solve the stair climbing problem [11], it does not entirely resolve the energy efficiency of the large and cumbersome wheelchair body since there are two decoupled running mechanisms in the wheelchair.

Several robots with curved legs [14,15] were developed, all inspired from animals in nature, to go over rough terrains including stairs. However, while those robots successfully go over the obstacles and climb the steps, they all compromise the comfort of the ride which is of importance to a patient in a wheelchair. They can travel very fast, but safety is more important than speed when it comes down to the mobility of a wheelchair.

The realization of the tri-wheel mechanism started by proposing the Loper Robot [16] with a particular design of the Tri-lobe wheel where each wheel is cut off such to act as a cog while climbing the stairs. However, there are some drawbacks to the performance of their design including speed, stability, and robustness; for example, during the stair climbing tasks, flipping of the robot, and jarring movements would cause the robot to drive off the side of the steps. Following the same concept of star-wheel or tri-wheel, Quaglia et al. presented a particular wheelchair that explored a “wheel-leg” locomotion design that has an auto–adaptive locomotion system that passively switches between rolling on wheels and ‘stepping on legs' simply on the basis of local friction and dynamic conditions [17,18]. Although their design was an improvement of the Loper mechanism, they had to use many motors and the overall wheelchair weight and size increased due to the complexity of their design. However, to rotate the star-shape wheel, they used a gear pair with an additional motor to provide an epicyclic motion on stair-climbing mode. They also added a complex tracking system to the front axle of the wheelchair to improve performance [18], which is not necessary if we incorporate the building codes of step sizes into the design.

The aim of this project is to design a universal stair-climbing transmission for wheelchairs that can be used on any set of ADA-approved stairs without requiring additional facilities [8]. This transmission mechanism allows the user to travel up or down stairs, thereby enabling them to participate in everyday activities like others without mobility issues. The important advantages of our proposed designs are safety, compactness and size, less weight, fewer actuators and sensors, simpler control systems, modular systems, energy efficiency, and robustness. With all the above objectives in mind, two design concepts for stair-climbing mechanisms are investigated or researched to create a universal transmission for the wheelchair. The remainder of the paper is organized as follows: Section 2 describes the design concepts and related kinematic analysis. Section 3 discusses the concept selection and analyses for prototyping and presents the prototype assembly and its testing performance. Finally, concluding remarks and future work are addressed in Sec. 4.

To design a stair-climbing wheelchair, a few design constraints were considered and maintained at the beginning of this project. First, a motorized wheelchair should smoothly travel on a flat surface, i.e., forward, backward, and turning. Second, the transmission system of the motorized wheelchair should be transformed to put the wheelchair on climbing mode and help prevent any rollback while climbing. Third, the system should be designed for the size of the standard stairs as specified by city building codes [8]. Fourth, it is assumed a motion plate for the wheelchair seat had been made with the idea that when the wheelchair climbs the stairs the user would stay level with the ground as a way to keep the user comfortable and safe. Note that the seat leveling mechanism is not the scope of this paper and the design of the wheelchair transmission system is of our focus in this research.

In terms of prototyping, comparing the commercial wheelchair size to the size of a standard step allowed the determination of the scaling size that was applied to both the staircase built and to the wheel system made. Before manufacturing a prototype, solidworks software is used for the design and analysis of the staircase and transmission system of the wheelchair. The finite element analysis has been conducted on the chosen concept to ensure that the transmission system can carry the exerted loads in both translation and stair-climbing modes. In this section, two feasible concepts are introduced followed by commenting on the control system.

where

N_r = number of teeth on ring gear

N_p = number of teeth on planetary gears

$NS$ = number of teeth on sun gear

N = number of planetary gears

Equations (1)–(3) work together to ensure that the system will not fail kinematically due to any unwanted gear interactions. Additionally, the pitch diameter of the gears must be equal, or the gears will not mesh correctly and create interference.

The translational speed of the wheelchair is another important parameter that should be considered in the kinematic calculations of the planetary mechanism. To obtain the correlation between the rotational speed of the sun, carrier, and planet gears, the superposition method in Table 1 allows the calculation of the final output speed of the system [19]. In this table, x and y are hypothetical variables that can be obtained for different kinematic scenarios of the system.

To make the wheelchair ascend and descend a staircase, there must be a way to regulate when ground motion or when traversing motion is required. Planetary gears are a unique mechanism due to their two-degree-of-freedom motion meaning that a planetary train requires two inputs. For both modes of transportation, the speed of the sun gear is determined by the user as the sun gear is directly affected by the motor; what differentiates the types of transportation is that for ground mode there is no input rotational speed for the carrier and for stair-climbing mode there is no input speed for the ring gear. In translation mode, the weight of the wheelchair assures the carrier stays stationary while the planets and connecting gear trains all rotate by the Sun leading to the rotation of the wheels and eventually traversing motion. However, in stair-climbing mode, the ring gear is fixed by a braking system and the planets along with the carrier rotate in an epicyclic fashion over the stairs. This will be explained further in Sec. 3.

In terms of sizing, Eqs. (1) to (5) were used to ensure that the ring gear and carrier would be able to function properly without interference with the stairs during our design iterations. Figures 3 and 4 show the transmission mechanism design of the tri-wheel planetary gear system. As shown in Fig. 4, the gear Aux 1, Aux 2, and wheel are mounted on a star shaped carrier, in which the entire carrier subassembly is connected to three planets. The Aux 1 gear is connected to the planet which is meshed with the Aux 2 that is connected to the rugged wheel. In fact, there is a gear train from the planet to the output of the rugged wheel.

The configuration of the tri-wheel planetary gear mechanism in Figs. 3(a) and 3(b) show the one in the traverse mode on the ground while Fig. 3(c) shows the configuration in the climbing mode. In Fig. 4, the Isometric view of the tri-wheel planetary gear mechanism is shown with only one out of three rugged wheels for a better demonstration of the assembly. In contrast with other research [18], only one motor is needed to trigger the Sun gear on each axle; therefore, in our design, the number of motors required for the two transversal modes is reduced which decreases the overall wheelchair weight, size, and cost while increasing the reliability.

Among all the designs to travel on rough terrains [6,7], we are inspired by a Curved Spoke Tri-Wheel Design [15] with a focus on optimizing kinematic parameters such as the radius of the center circle, radius of curvature of each spoke, and angle between the radius of the inner circle and the radius of curvature of each spoke to clear steps efficiently. The mechanism includes a main body with a controller and two curved-spoke tri-wheels on the left and right, as depicted in Fig. 5. As seen in the figure, the aim was not to develop this design for a wheelchair but adopting it for a wheelchair in which comfort and safety are the main priorities would prove to be a challenge.

The design parameters are determined from the kinematic analysis for step clearing with no slippage. Based on this constraint the kinematic parameters can be determined with a system of algebraic equations. Figure 6 shows the free-body diagram of the kinematic analysis.

From these relations, the independent variables are all defined accordingly for a given staircase dimension. Although this design seems promising on the stairs, using this design for a wheelchair in translation mode on a straight surface won't be efficient due to vibration, especially in low-speed traveling.

Deriving from the Curved Spoke Tri-Wheel mechanism, a concept of a Variable Curved-Spoke Tri-Wheel is developed by our group. The design implemented the efficient step-clearing capabilities of the curved spoke tri-wheel to a variable wheel. The design could transform between wheel mode on ground translation and curved spoke tri-wheel on stair climbing operation. This transformation can be achieved by using a curved pin-slot mechanism in the center circle, actuated by a pinion gear at the end of the shaft, as shown in Figs. 7 and 8.

The main components of the variable curved-spoke tri-wheel design are shown in Fig. 7. In this design, the central axel is affixed to the Spider Base where all other components are mounted or connected to this part. The Slot Carrier is connected to the Pinion which by CW or CCW rotation causes the pins to slide up or down the slots, respectively. When the pins are at the upper position, the curved spokes are open for the stair climbing mode; and when the pins are at the lower position, the curved spokes are closed to become a circular wheel for the ground translation mode. Note that the pinion gear and the central axle are independent allowing the whole tri-wheel mechanism to rotate at either mode.

This concept attains all the advantages of a wheel for ground translation mode along with all the advantages of a curved-spoke tri-wheel mechanism for stair climbing mode. However, two actuators are needed to operate the system. There is a need for a stepper motor or servomotor to trigger pinion rotation to open or close the spokes. In addition, a motor is needed to rotate the central axle for moving forward or backward in either mode. In comparison with concept 1, we need double the actuators and sensors in this concept; one to tripper the pinion and the other one to rotate the axle. Having extra sensors and actuators are the main drawback of this concept leading us to stop pursuing this design to a full prototype. However, the transformation between a round wheel and a curved-spokes tri-wheel mechanism is a creative concept that we present in this article for the first time.

A complete functional diagram for a wheelchair with stair-climbing capability is demonstrated in Fig. 9. The wheelchair comprises of several components that work interchangeably to provide the stair-climbing feature. A battery is the power source; this power from the battery is transferred to the controller and the servo-amplifier. When the controller is activated by user input, the signal from the controller is transferred to the servo-amplifier that amplifies the signal and sends the current to the DC motors. The servo-amplifier is also responsible for controlling the torque and its direction supplied by the DC motors. Then the rotational speed and torque are transferred to the sun gear of the planetary mechanism. In the gear mechanism, the supplied torque is rationed to a design limit and then transfers this torque to the tri-wheel climbing mechanism that performs the actual climbing of the stairs. Because of the movement of the seat at an awkward angle as the wheelchair performs the climb, it is necessary to level the chair for the safety of the rider. Therefore, the wheelchair seat should have an adjustment mechanism to set the angle of the seat horizontally in the descending or ascending motion of the wheelchair. The part of the chair mechanism responsible for this balancing task is a gyroscope sensor. At the time when the braking system is triggered to fix the ring gear and to activate the climbing mechanism, the battery supplies power to a seat adjustment mechanism that levels the seat of the wheelchair as it climbs the stairs. The seat adjustment mechanism is not in the scope of this research and is not considered in our prototype; however, this can be proceeded as a four-bar mechanism in future research.

For the prototype, the scaled-down wheelchair utilizes the microcontroller VEX V0.5 Robotic Design System [20]. The electronics of the vehicle can be broken down into several components: motor, receiver, transmitter, and VEX microcontroller, as shown in Fig. 10. The control subsystem is the direct link between the vehicle and the human operator. The transmitter operates in two basic configurations, mode ‘23' or ‘12'. The vertical axis of the right stick on the transmitter was “Control Channel 2” and the vertical axis of the left stick was “Control Channel 3,” hence axes 2 and 3 are being used to drive [20]. Under Configuration “23” the left and right joystick on the transmitter controls both the left-axle and right-axle of tri-wheels, respectively. This control scheme assures the synchronization of the left and right sides of the vehicle which is necessary in the climbing mode. If the left- and right-side tri-wheels were to rotate out of sync, it would cause interference and destabilization during stair climbing. Hence Configuration “12” was selected for prototyping and testing. In this configuration, the transmitter uses only one joystick to control forward, reverse, and turning motions. This allowed both the right- and left-axle to rotate in sync while by using the Configuration “23,” the vehicle can move and turn on ground surface in the translation mode.

The decision matrix method has been used to choose between two concepts stated in Secs. 2.1 and 2.2. After considering both concepts and assessing the strengths and weaknesses of the two mechanisms, the tri-wheel design was chosen for further development, prototyping, and testing. While the curved-spoke wheel was also a highly plausible concept, the limitation of in-house manufacturability and the extra number of actuators were the main drawbacks that swayed us away from making a full prototype of the curved-spoke concept at this moment.

Once the concept of the tri-wheel planetary gear mechanism was selected for prototyping, several iterations of this concept were built and tested with each test presenting a new problem that needed to be fixed. For example, Fig. 11 shows the second iteration of the tri-wheel design without considering the effect of the weight of the materials. The very first iteration was based on only kinematics to understand and assess the desired motion where the measurements of the stairs were not considered.

To test the design on an actual stair, a scaled-down wooden staircase is built according to the building code [4]. In a typical state building, the specification of stairs is as follows: the run should vary between 8-1/4″ to 9″, while the rise is between 8″ to 8-1/4″ and the nosing is between 1″ and 1-1/2″. In the first iteration, when testing began the system did not climb the stairs due to interferences between the ring gear and the ledge nosing of the steps. The interference issue has been addressed by changing the geometry of the ring gear and carrier in the second iteration of the design. However, as seen in Fig. 11, the second iteration was slightly bulky and heavy which required much more torque to climb up. In other words, although it kinematically satisfied the constraints, the generated output torque was not satisfactory.

In kinematic analysis of the planetary system, Eqs. (1)–(3) are applied and the specifications of gears are obtained as shown in Table 2. The dimensions of the planetary tri-wheel mechanism are directly related to this analysis that we need to ascertain to clear the steps with no interference. The gear of Aux 1 is connected to the planet and the gear of Aux 2 is meshed with Aux 1 that is connected to the rugged wheel. The gears of Aux 1 and Aux 2 are all mounted on a star shape carrier. Each Aux 1 gear and the corresponding planet are mounted on the same shaft; similarly, Aux 2 gear and the corresponding rugged wheel are mounted on the same axle.

The superposition method from Table 1 allows the calculation of the final output speed of the system. The speed of the DC Motor that is connected to the sun gear is variable and can increase from zero to its maximum by the user's input. For instance, assuming an input sun speed of 100 rpm, Eqs. (5) to (7) are derived to determine the speed of each component in the stair-climbing mode. The results of the calculated rotational speeds are shown in Table 2. One can obtain the linear velocity of the wheelchair using the information of Table 2. For example, the wheelchair has a velocity of 3.6 in/s in the translation mode in this case.

A kinetic analysis is conducted before manufacturing the prototype of the wheelchair transmission system. An actual motorized wheelchair has a weight of 250 lbf combined with the additional patient assumed to be approximately 500 lbf altogether. For the scaled-down prototype (1:4), the weight of 125 lbf is considered for the force analysis of the wheelchair for a critical situation climbing over an inclined surface with an angle equivalent to the grade of standard stairs. In the kinetic analysis, the coefficient of friction between rugged wheels and stairs is assumed 0.2, and the grade of $tan∝=1.138$ is obtained for the standard stairs by using the building code. The calculation shows that the minimum torque of 5.5 lbf-in is required to apply on the Sun gear to facilitate climbing. Thus, the core component of the tri-wheel transmission mechanism which is the planetary gear system should be able to carry such load. Next, the finite element analysis (FEA) has been conducted for both translation and climbing modes to ensure the strength and safety of the system.

Figures 12 and 13 show the results of FEA for both translation and climbing cases. The material is assumed to be ABS and the model is meshed with tetrahedral solid elements. In our simulations, the input torque is applied to the shaft surface of the Sun gear and proper boundary conditions, including the contact between gear teeth, are considered. As seen from Figs. 12(a) and 13(a), the Sun gear would be the most critical component where the maximum von-Mises stress occurs between the teeth of the Planets and Sun gears. The maximum stress obtained in Figs. 12(a) and 13(a) were 1376 psi in translation mode and 3052 psi in climbing mode, respectively. As expected, the climbing mode is the most critical case, and the maximum stress of 3052 psi should be used as a threshold stress to properly select the material for manufacturing. For instance, the ABS of the UltiMaker 3D-Printer machine has a yield strength of 4.93 kpsi whereas it is 47.9 kpsi for low-carbon steel alloy. Therefore, the factor of safety of the system obtained is about 1.6 or 15.7 by choosing ABS or Steel alloy materials, respectively.

For the prototype, the ABS material was selected since it was accessible and could be easily manufactured during multiple design iterations of the product; however, for the actual wheelchair, the metal alloy is recommended to assure higher safety and durability.

In Figs. 12(b) and 13(b), the total displacements are plotted for both the translation and climbing modes. In the translation mode, all the gears are rotating about their axes, but the carrier is stationary whilst allowing the gear trains to rotate the rugged wheels. However, in the climbing mode, the Ring gear is fixed, and the Sun and Planets are rotating while also providing the rotation of carrier or tri-wheel to facilitate the climbing action. The total deformation in each mode is compatible with the physics and the experiment which verifies the correctness of boundary conditions in the FEA simulations of both modes.

The CAD model of the Tri-wheel Planetary Gear Mechanism is finalized after all the kinematic and kinetic analyses as shown in Fig. 14. Note that this is just a prototype of the transmission system of the actual wheelchair to prove the design concept. After multiple design iterations and tests, the design of the tri-wheel planetary gear system was finalized to correct all previous concerns and underwent some design changes to conserve materials and optimize the weight. For the prototype, the transmission system of the tri-wheel planetary gear mechanism was built and assembled in house, as shown in Fig. 15, while the other components were outsourced to employ in assembly, such as the control unit, motors, etc. Figure 15 shows the final assembly of the tri-wheel planetary system after manufacturing. Four of these assembled units are needed in a four-wheel-drive wheelchair while two units can be utilized in a front- or rear-wheel-drive wheelchair.

Figure 16 shows the final prototype of an entire vehicle after manufacturing and assembly. During prototype iterations, multiple tests have been conducted to ensure all components function properly. To be able to test the prototype, a scaled-down wooden staircase was built according to the building code. As seen in Fig. 16, the planetary tri-wheel system was tested and successfully climbed the wooden staircase.

During testing of the prototype, one of the challenges was the braking system that is supposed to trigger and switch between translation and climbing modes. In the prototype stage, a manual braking system is designed as shown in Fig. 17, even though an automated braking system should be considered in an actual wheelchair. Since the Ring gear should be fixed in climbing mode, an L-shape bracket with a screw is manufactured and assembled on the chassis as shown in Fig. 17. By fastening the screw to one of the side holes of the Ring gear, it will be secured to the chassis preventing the Ring gear from rotating which will facilitate the climbing mode.

Despite the successful manufacturing and testing of a planetary tri-wheel transmission system, there is always room for improvements, especially in manufacturing of the prototype. As future work, a seat stabilizer, which will level the patient seat on an inclined ramp, is necessary in a stair-climbing wheelchair for efficient and safe locomotion over the stairs. The seat stabilizer mechanism in conjunction with the planetary tri-wheel transmission system will make a complete and safe stair-climbing wheelchair. Design and build an adaptive control system to automatically switch between translation and stair-climbing mode would be also another avenue to explore in future.

Many urban places are not accessibility friendly necessitating the use of special wheelchairs to cope with stairs for daily locomotion of the disabled. To make a building accessible, there are extra accessories and facilities to utilize or mount on stairs; however, all those solutions are not only expensive but also may not work in the case of a power outage or a fire inside the building. Furthermore, providing such facilities for all exits on every floor of a high-rise building, for instance, is almost impossible. To solve this universal problem for the disabled, it would be very desirable that a wheelchair has the ability of stair climbing. In this article, two concepts have been proposed to design a stair-climbing wheelchair: Tri-Wheel Planetary Mechanism, and Variable Curved Spoke Wheel. The more feasible concept of the tri-wheel system in conjunction with planetary gears was chosen to pursue the detailed design, analysis, prototyping, and field test. During the manufacturing and testing of the prototype, multiple steps were taken to improve the quality of motion pertaining to both translation and stair-climbing modes. The test results of the scaled-down prototype show that the Tri-Wheel Planetary Mechanism successfully negotiated or climbed the stairs and is promising to be adopted for a stair-climbing wheelchair. This upgrade will give the disabled a peace of mind and the ability to go everywhere during their daily lives without any external help or facility. On the other hand, this design is cost and energy efficient in the sense that it will be un-necessary to build accessible areas and facilities for public places and buildings. With the stair-climbing design upgrade, a person with a disability in a wheelchair would treat and feel like other travelers in the city.