Development of Power-Assist Device for a Manual Wheelchair Using Cycloidal Reducer

: This paper presents the design process and driving performance test results of a power-assist module to which a cycloidal reducer is applied in order to convert a manual wheelchair into an electric wheelchair. The types of electriﬁcation modules currently used to electrify manual wheelchairs include front-mounted, rear-mounted, and powered wheels. These assist devices are either difﬁcult to carry and transport independently or require excellent hand dexterity to operate. To overcome this problem, a cycloidal reducer with no pin roller, and a novel cycloidal curve were designed to develop a small and easy-to-handle power-assist module that was tested by installing this reducer to a manual wheelchair. As a result of the test, the maximum speed of the wheelchair was 6 km/h, the maximum slope that this wheelchair can climb is 20%, and 0.358 Ah was consumed while the wheelchair moved 360 m in the current consumption test. This showed that it is possible to develop a small-sized power-assist module. In addition, the user can easily electrify the manual wheelchair by adding a small weight without replacing the manual wheel. The power-assist module consists of a DC servo motor, cycloidal reducer, battery, and joystick.


Introduction
Manual and electric wheelchairs are commonly used mobile devices by the disabled and elderly.Manual wheelchairs have mainly been used for short distances on flat ground or with good road conditions.However, more than 50% of manual wheelchair users complain of back and shoulder pain caused by prolonged wheelchair usage [1][2][3].A power wheelchair, in contrast, consists of a motor and rechargeable battery, and is controlled using a joystick located on the armrest; hence, it does not require muscle strength and can travel long distances.However, the weight of the wheelchair is significantly high, and its transportation is difficult.Most reducers for power wheelchairs use worm gears and comprise of characteristics such as self-locking mechanism and high reduction ratio.However, reducers are not suitable for power-assist devices (PADs) because of their low efficiency and large space requirement.The burden on the upper extremities experienced during propulsion can be reduced by adding a motorized device to a PAD that can supply power to the manual wheelchair [3].Furthermore, it could be effective in compensating the limited capabilities of manual wheelchairs.
PADs for manual wheelchairs combine the advantages of manual and electric wheelchairs, and have the potential to improve the mobility, community participation, and well-being of users.Three types of PADs currently in use are: front-and rear-mounted, and powered wheels [3].The front attachment configuration consists of Electric 2 [4] from Batec Mobility, and Firefly 2.5 [5] from Rio Mobility.This configuration has the advantage that the user can use it as a motorcycle at high speed (>10 km/h) by attaching a separate drive module to the front of the wheelchair; however, it is difficult to lift, carry, and transport because of the front mounting structure.Rear-mounted attachments for wheelchairs are devices mounted on the rear axle of manual wheelchairs.SmartDrive [6] is a rear-mounted PAD controlled by a dial.By turning the speed control dial on the wheelchair frame, the user can start the motion, stop the device, and set the speed.The Smoov wheel [7] has a one-wheeled design similar to SmartDrive and a frame-mounted knob to control the wheelchair speed.These products are difficult to brake and stop, and the time required to become accustomed to them is long.
Powered wheels can also replace the traditional wheels of manual wheelchairs, and can be controlled interactively using a joystick or direct push rims.Powered wheels, such as E-fix [8], replace conventional wheels and allow users to control a wheelchair using a joystick with ease.Seong [9] designed a small-sized planetary gear and developed a power wheel that can be applied to a manual wheelchair.Pushrim-activated power-assist wheels (PAPAWs) are another type of powered wheels consisting of a built-in force sensor that detects the user input force acting on the pushrims.When the user activates the pushrim, the speed of the wheelchair is proportional to the input force.Examples of PAPAWs include e-motion [10] and JWII [11] wheels.Nam [12] proposed an input force measurement system for PAPAW and the driving torque of the measured force in which the user pushes the handrim using only an angle sensor.
A reducer is a type of mechanical energy conversion device that can amplify torque by reducing the rotational speed of the motor.In particular, the reducers in which the input and output shaft are coaxial include harmonic drives, planetary gears, and cycloidal reducers.Cycloidal reducers have been used in power transmissions, boats, cranes, pumps, and prosthetic hands [13].Cycloidal reducers can feature low backlash, high efficiency, low noise, a high-reduction, and high torque capacity unlike harmonic drives [13][14][15].Shin [16] proposed an exact approach to the cycloid disk by means of the principle of the instant velocity center.Lin [17] presents a method for kinematic error analysis and tolerance design of cycloidal gear reducers.The conventional cycloidal reducer consists of pin rollers, and multiple contacts are established between the pin rollers and cycloidal disks, making it difficult to manufacture.However, because the proposed reducer has a single-contact structure, it is insensitive to tolerances during manufacturing, and the structure of the reducer is simple because there are no pin rollers required.
In this study, a novel gear curve design method for a cycloidal reducer with no pin rollers and a single-contact structure was proposed, and a thin cycloidal reducer with a maximum speed of 6 km/h was developed by analyzing the dynamic characteristics of the reducer according to the reduction ratio.The cycloidal reducer, DC servo motor, and electromagnetic brake comprise a power unit for driving a wheelchair, and a user manual wheel can be inserted into the output shaft of the power unit.Driving performance tests such as a ramp driving test, maximum speed test, and durability test were performed to determine user convenience and stability.It was confirmed that the PAD with the designed cycloidal reducer is effective in the performance of a manual wheelchair.

Generating Cycloidal Tooth Profile
In this section, we present a practical method for the design of the cycloidal reducer for the PAD that can be installed on a manual wheelchair.The input shaft drives an eccentric bearing that in turn drives the cycloidal disk in an eccentric.The perimeter of this disk is geared with several pin rollers and has a series of output shaft pins in the holes on the disk.These output shaft pins directly drive the output shaft when the cycloidal disk rotates.The direction of rotation of the disk and output is opposite to that of the input shaft.
In general, the cycloidal reducer, cycloidal disks and pin rollers are in contact at the same number of points as the number of pin rollers.However, in the proposed reducer, the cycloidal disk is engaged with an epitrochoid curve called the housing gear corresponding to the housing.In addition, the cycloidal disk and housing gear have a single contact point, similar to a general involute gear (Figure 1). the cycloidal disk is engaged with an epitrochoid curve called the housing gear corresponding to the housing.In addition, the cycloidal disk and housing gear have a single contact point, similar to a general involute gear (Figure 1).An epicycloid is a path traced by a point on the rolling circle that rotates outside the base circle.Similarly, an epitrochoid is a geometric curve traced by a fixed point inside a rolling circle that rotates around the perimeter of the base circle.
The parametric equations for an epitrochoid can be given: where  is the radius of the interior circle called the base circle,  is the radius of the exterior circle called the rolling circle, k is the distance from the center of the rolling circle, and  is geometrically the polar angle of the center the rolling circle.When the number of teeth on the cycloidal disk is , the ratio of the radius of the interior and exterior circles is  / .
The first parametric derivatives of Equation ( 1) with respect to  are given by: The equidistant curve, frequently called a parallel curve, is a curve that is displaced from Equation (1) by a constant offset.That curve is calculated as follows [18]: ℎ

𝑥 𝑡 𝑦 𝑡
where   ,   is a point on the epitrochoid curve and (  ,   ) is a point on the parallel curve (equidistant curve) by an offset distance ℎ.  is the radius of the pitch circle of the parallel curve and is calculated using   /2.Where  and  are the radius of the addendum and dedendum circle of the equidistant curve, respectively (Figure 2).An epicycloid is a path traced by a point on the rolling circle that rotates outside the base circle.Similarly, an epitrochoid is a geometric curve traced by a fixed point inside a rolling circle that rotates around the perimeter of the base circle.
The parametric equations for an epitrochoid can be given: where r b is the radius of the interior circle called the base circle, r r is the radius of the exterior circle called the rolling circle, k is the distance from the center of the rolling circle, and t is geometrically the polar angle of the center the rolling circle.When the number of teeth on the cycloidal disk is Z, the ratio of the radius of the interior and exterior circles is The first parametric derivatives of Equation (1) with respect to t are given by: The equidistant curve, frequently called a parallel curve, is a curve that is displaced from Equation (1) by a constant offset.That curve is calculated as follows [18]: (3) where (x(t), y(t)) is a point on the epitrochoid curve and (x D (t), y D (t)) is a point on the parallel curve (equidistant curve) by an offset distance h.r p is the radius of the pitch circle of the parallel curve and is calculated using (r a + r d )/2.Where r a and r d are the radius of the addendum and dedendum circle of the equidistant curve, respectively (Figure 2).The tooth profile can have various shapes of gear curves having the same pitch circle according to the offset distance.To realize this design approach, the concept of tooth thickness ratio (TTR) was introduced.The TTR is defined as the ratio the tooth occupies on the pitch circle, and is calculated by dividing the tooth thickness by the sum of the tooth thickness and the space width.The tooth thickness ( ) is the shortest distance between the two points on the gear curve passing through the pitch circle, and the space width ( ) is the shortest distance of the space between two lobes through the pitch circle.The tooth thickness and space width are calculated as shown in Equation (5).

𝑤 2𝑟 sin 𝜃
where  is tooth thickness angle.The TTR is obtained as follows: In all gear ratios, cycloidal gears could be designed using a TTR ranging from 0.4 to 0.6.In this study, considering the strength of the housing gear and cycloidal disk, the TTR was decided to be 0.5, which makes the tooth thickness and the space width equal, and then  becomes /2.The coordinate values of point  in Figure 3 become  cos / 2 ,  sin /2 , and the offset is expressed as the pitch circle radius, as shown in Equation (7).
Equation ( 4) is replaced with Equation ( 7) and the coordinates of point .Equation ( 3) can be replaced with Equations ( 1) and ( 2) as follows: The tooth profile can have various shapes of gear curves having the same pitch circle according to the offset distance.To realize this design approach, the concept of tooth thickness ratio (TTR) was introduced.The TTR is defined as the ratio the tooth occupies on the pitch circle, and is calculated by dividing the tooth thickness by the sum of the tooth thickness and the space width.The tooth thickness (w t ) is the shortest distance between the two points on the gear curve passing through the pitch circle, and the space width (w s ) is the shortest distance of the space between two lobes through the pitch circle.The tooth thickness and space width are calculated as shown in Equation ( 5).
where θ is tooth thickness angle.The TTR is obtained as follows: In all gear ratios, cycloidal gears could be designed using a TTR ranging from 0.4 to 0.6.In this study, considering the strength of the housing gear and cycloidal disk, the TTR was decided to be 0.5, which makes the tooth thickness and the space width equal, and then θ becomes π/2Z.The coordinate values of point P in Figure 3 become r p cos(π/2Z), r p sin(π/2Z) , and the offset is expressed as the pitch circle radius, as shown in Equation (7).
sin /2  1   sin /2   sin  (10) By substituting Equation (10) into Equation ( 7), the following expression is obtained: Since the  and ℎ in Equation ( 11) are unknown values, a numerical method such as the Newton-Raphson method [19] is required for an arbitrary offset distance ℎ to obtain the value of the polar angle .By substituting the calculated  value into Equation ( 4), the temporary coordinates of point  is calculated, and the temporary tooth thickness angle  is obtained by tan  / in Equation ( 4).Then, the temporary TTR  is calculated by Equation ( 6) and the iteration is stopped when   is within a given tolerance 10 .Figure 4 shows tooth profiles, as TTR increased, when the number of teeth = 49, module = 1.0 and the distance  = 0.45.All gear profiles have the same pitch circle diameter and addendum, but each profile has a different base circle, rolling circle, and offset distance.Equation ( 4) is replaced with Equation ( 7) and the coordinates of point P.
Afterwards, Equations ( 8) and ( 9) are multiplied by −r r sin t + k sin((Z + 1)t) and r r cos t − k cos((Z + 1)t), respectively, and then two equations are added.r r = r p k sin(π/2Z − (Z + 1)t) r p sin(π/2Z − t) − kZ sin(Zt) (10) By substituting Equation (10) into Equation ( 7), the following expression is obtained: Since the t and h in Equation ( 11) are unknown values, a numerical method such as the Newton-Raphson method [19] is required for an arbitrary offset distance h to obtain the value of the polar angle t.By substituting the calculated t value into Equation ( 4), the temporary coordinates of point P is calculated, and the temporary tooth thickness angle θ t is obtained by tan −1 (y D /x D ) in Equation ( 4).Then, the temporary TTR δ t is calculated by Equation ( 6) and the iteration is stopped when δ t − δ is within a given tolerance 10 −3 .
Figure 4 shows tooth profiles, as TTR increased, when the number of teeth = 49, module = 1.0 and the distance d = 0.45.All gear profiles have the same pitch circle diameter and addendum, but each profile has a different base circle, rolling circle, and offset distance.For the cycloidal disks and housing gear to mesh, the TTRs ratio of the two gears and module must be the same.For the number of teeth of cycloidal disk  and the number of teeth of housing gear  , the pitch circle diameters of the cycloidal disk and housing gear are as follows: where,  ,  are the pitch circle diameters of the cycloidal disk and housing gear, respectively, and the difference of the teeth between the cycloidal disk and housing gear is 1.When the center distance between the housing gear and cycloidal disks is the eccentricity , the eccentricity can be determined as half a module [20]. (13)

Design of Cycloidal Reducer
In the conventional cycloidal reducer, all the teeth are in contact with the pin rollers, however, for the proposed reducer there is only a single-contact condition between the housing gear and cycloidal disks, hence the different dynamic characteristics when compared with the existing cycloidal reducer.Therefore, it is important to analyze the dynamic characteristics of the proposed reducer.In addition, a dynamic simulation was performed using an MSC ADAMS 12.0 (MSC Software, Newport Beach, CA, USA) multibody dynamics analysis program for even and odd reduction ratios.The even and odd reduction ratios used in this study were 50:1 and 49:1, respectively.
In general, when performing a dynamic analysis, a 3D CAD program such as Solid-Works converts the model to parasolid format, and the converted model is loaded into the ADAMS.However, in the case of a very diversified curve, such as a cycloidal gear, the gear surface of the parasolid-converted model cannot be accurately represented for simulation, making accurate contact force analysis difficult.For a more accurate dynamic simulation, using the cycloidal gear design program developed in the laboratory, the teeth of the cycloidal disk and housing gear were fabricated at 120 points in a tooth and the gear curve was expressed as a polyline.Therefore, the greater the number of discrete points on the tooth profiles of the cycloidal gears, the more accurate are the contact analysis results.For the cycloidal disks and housing gear to mesh, the TTRs ratio of the two gears and module must be the same.For the number of teeth of cycloidal disk Z 1 and the number of teeth of housing gear Z 2 , the pitch circle diameters of the cycloidal disk and housing gear are as follows:

𝑒 𝑚 2
where, d i p , d e p are the pitch circle diameters of the cycloidal disk and housing gear, respectively, and the difference of the teeth between the cycloidal disk and housing gear is 1.When the center distance between the housing gear and cycloidal disks is the eccentricity e, the eccentricity can be determined as half a module [20].

Design of Cycloidal Reducer
In the conventional cycloidal reducer, all the teeth are in contact with the pin rollers, however, for the proposed reducer there is only a single-contact condition between the housing gear and cycloidal disks, hence the different dynamic characteristics when compared with the existing cycloidal reducer.Therefore, it is important to analyze the dynamic characteristics of the proposed reducer.In addition, a dynamic simulation was performed using an MSC ADAMS 12.0 (MSC Software, Newport Beach, CA, USA) multi-body dynamics analysis program for even and odd reduction ratios.The even and odd reduction ratios used in this study were 50:1 and 49:1, respectively.
In general, when performing a dynamic analysis, a 3D CAD program such as Solid-Works converts the model to parasolid format, and the converted model is loaded into the ADAMS.However, in the case of a very diversified curve, such as a cycloidal gear, the gear surface of the parasolid-converted model cannot be accurately represented for simulation, making accurate contact force analysis difficult.For a more accurate dynamic simulation, using the cycloidal gear design program developed in the laboratory, the teeth of the cycloidal disk and housing gear were fabricated at 120 points in a tooth and the gear curve was expressed as a polyline.Therefore, the greater the number of discrete points on the tooth profiles of the cycloidal gears, the more accurate are the contact analysis results.
The contact stiffness between the cycloid disk and housing gear can be calculated using [21]: Appl.Sci.2023, 13, 954 7 of 14 where K hc represents the contact stiffness between the cycloidal gear and housing gear.r c is the radius of curvature of the cycloidal tooth profile, E c and ν c denote Young's modulus and Poisson's ratio of the material used in the cycloidal disk, respectively, and E h and ν h are the corresponding properties for the material used to make the housing gear, respectively.
Here, H is an adjusting coefficient used to control the magnitude of the contact stiffness.
The description of parameters with values is shown in Table 1.When the input shaft rotates once at a low speed (10 deg/s), a vibration is generated and transmitted to the ground owing to the contact force between the cycloidal disk and housing gear, and the results differ depending on the reduction ratio (Figure 5).
where  represents the contact stiffness between the cycloidal gear and housing gear. is the radius of curvature of the cycloidal tooth profile,  and  denote Young's modulus and Poisson's ratio of the material used in the cycloidal disk, respectively, and  and  are the corresponding properties for the material used to make the housing gear, respectively.Here,  is an adjusting coefficient used to control the magnitude of the contact stiffness.The description of parameters with values is shown in Table 1.When the input shaft rotates once at a low speed (10 deg/s), a vibration is generated and transmitted to the ground owing to the contact force between the cycloidal disk and housing gear, and the results differ depending on the reduction ratio (Figure 5).At an even reduction ratio (50:1), the two disks are aligned exactly 180 • to each other; however, the contact points of each disks have a half-tooth phase difference based on the housing gear owing to the odd teeth of the housing gear.Therefore, the resultant force in the x-and y-axis directions of the two contact forces cannot be canceled, leaving a residual force and causing vibration.Such vibrations may cause discomfort and fatigue when a user travels (Figure 6).At an even reduction ratio (50:1), the two disks are aligned exactly 180° to each other; however, the contact points of each disks have a half-tooth phase difference based on the housing gear owing to the odd teeth of the housing gear.Therefore, the resultant force in the x-and y-axis directions of the two contact forces cannot be canceled, leaving a residual force and causing vibration.Such vibrations may cause discomfort and fatigue when a user travels (Figure 6).In contrast, for an odd reducer ratio (49:1), the contact points between the cycloidal disks and housing gear exhibit the same phase on the housing gear and are completely symmetrical with each other, and the resultant forces cancel each other in the x-and yaxis directions.This implies that no vibration was transmitted to the ground.
Dynamic simulations are required even at high speeds because wheelchairs move at low and high speeds.When the wheelchair user moves at a maximum speed of 6 km/h, the motor rotates at approximately 3000 rpm.Therefore, this was set as the high-speed simulation condition.The speed of the reducer was gradually increased from standstill to the maximum speed for 2 s and then maintained at the maximum speed, and the simulation was conducted for 3 s.At an even reduction ratio, the vibratory force generated at the center of the reducer increased for up to 2 s, after which a similar pattern was observed.However, there was no vibration observed at an odd reduction ratio, similar to the lowspeed simulation results (Figure 7).The reduction ratio was decided to be 49:1 based on the results of the vibration simulation.Eccentricity  and the distance k of the designed cycloidal reducer were 0.5 mm In contrast, for an odd reducer ratio (49:1), the contact points between the cycloidal disks and housing gear exhibit the same phase on the housing gear and are completely symmetrical with each other, and the resultant forces cancel each other in the x-and y-axis directions.This implies that no vibration was transmitted to the ground.
Dynamic simulations are required even at high speeds because wheelchairs move at low and high speeds.When the wheelchair user moves at a maximum speed of 6 km/h, the motor rotates at approximately 3000 rpm.Therefore, this was set as the high-speed simulation condition.The speed of the reducer was gradually increased from standstill to the maximum speed for 2 s and then maintained at the maximum speed, and the simulation was conducted for 3 s.At an even reduction ratio, the vibratory force generated at the center of the reducer increased for up to 2 s, after which a similar pattern was observed.However, there was no vibration observed at an odd reduction ratio, similar to the lowspeed simulation results (Figure 7).At an even reduction ratio (50:1), the two disks are aligned exactly 180° to each other however, the contact points of each disks have a half-tooth phase difference based on the housing gear owing to the odd teeth of the housing gear.Therefore, the resultant force in the x-and y-axis directions of the two contact forces cannot be canceled, leaving a residua force and causing vibration.Such vibrations may cause discomfort and fatigue when a user travels (Figure 6).In contrast, for an odd reducer ratio (49:1), the contact points between the cycloida disks and housing gear exhibit the same phase on the housing gear and are completely symmetrical with each other, and the resultant forces cancel each other in the x-and y axis directions.This implies that no vibration was transmitted to the ground.
Dynamic simulations are required even at high speeds because wheelchairs move a low and high speeds.When the wheelchair user moves at a maximum speed of 6 km/h the motor rotates at approximately 3000 rpm.Therefore, this was set as the high-speed simulation condition.The speed of the reducer was gradually increased from standstill to the maximum speed for 2 s and then maintained at the maximum speed, and the simula tion was conducted for 3 s.At an even reduction ratio, the vibratory force generated at the center of the reducer increased for up to 2 s, after which a similar pattern was observed However, there was no vibration observed at an odd reduction ratio, similar to the low speed simulation results (Figure 7).The reduction ratio was decided to be 49:1 based on the results of the vibration sim ulation.Eccentricity  and the distance k of the designed cycloidal reducer were 0.5 mm The reduction ratio was decided to be 49:1 based on the results of the vibration simulation.Eccentricity e and the distance k of the designed cycloidal reducer were 0.5 mm and 0.45 mm, respectively.Table 2 lists the design results of the cycloidal reducer.The width of the cycloidal disks is 5 mm, and the diameter of the outer rollers, rotating around the holes on the cycloidal disk, is 6 mm.

Power-Assist Device
In this section, using the designed cycloidal reducer, we configure the PAD.A DC servomotor with a rated output of 200 W, rated speed of 3000 rpm, and rated torque 0.64 Nm was used for the drive motor.The electromagnetic brake used was the BXW-03-12S (Miki Pulley, Kanagawa, Japan) with a rated capacity of 9 W, maximum rotational speed of 5000 rpm, and static friction torque of 1.5 Nm, that maintains the wheelchair at a standstill when on a ramp.The motor speed control can obtain an enhanced quadrature encoder pulse (eQEP) using a TMS320F28035 (Texas Instruments, Dallas, TX, USA) chip installed on the rear of the motor.The power unit consists of the motor, brake and cycloidal reducer.The weight of the power unit was 2.5 kg.The size of the cycloidal reducer was 70 mm in diameter and 34.5 mm in thickness, and its weight was 0.8 kg.The battery was packed with 63 cylindrical Li-ion batteries (2.6 Ah, 3.7 V) and hung under the wheelchair seat, and its specifications are 25.9 V, 23.4 Ah, and 4.5 kg.A button was installed at the end of the output shaft on the power unit, and when pressed, it releases the wheel when loading the wheelchair into a vehicle.
Figure 8 shows the configuration of the power unit.A block between the motor and reducer connects the power unit to the wheelchair frame.There is a motor driver board located on the back of the motor.The motor and reducer are connected in series coaxially, and the electromagnetic brake is connected to the motor via a timing belt.Figure 9 shows the PAD consisting of the power unit, battery, and joystick.Unlike the position where the manual wheel was installed, the PAD is mounted behind the back through a block for combining with the frame.In addition, the PAD allows the reclining of the back and helps with the easy installation of the manual wheel.

Results
In this section, results of a performance test for a manual wheelchair with the PAD installed are presented.The dynamic performance of the proposed cycloidal reducer was tested according to the Korean standard (KS B 7300:2016), and the results are listed in Table 3.The efficiency of the reducer was in the range of 77-78.21%when the input shaft rotation speed was 2000 rpm and the output shaft torque was 30 Nm.The angle-transmission error was calculated as the difference between the output shaft and input shaft rotation angles divided by the reduction ratio.The backlash of the reducer was 3.84 arc min.

Results
In this section, results of a performance test for a manual wheelchair with the PAD installed are presented.The dynamic performance of the proposed cycloidal reducer was tested according to the Korean standard (KS B 7300:2016), and the results are listed in Table 3.The efficiency of the reducer was in the range of 77-78.21%when the input shaft rotation speed was 2000 rpm and the output shaft torque was 30 Nm.The angle-transmission error was calculated as the difference between the output shaft and input shaft rotation angles divided by the reduction ratio.The backlash of the reducer was 3.84 arc min.To test the operational characteristics of the developed PAD, a driving operation was conducted on a 10.5 • slope, as shown in Figure 10.It was confirmed that the driving torque of the electric assist device was sufficient for a user weighing 100 kg to easily drive up the slope.The maximum slope that the wheelchair could ascend was 20%.
The maximum speed test for a manual wheelchair with the PAD installed was performed on a horizontal surface using the ISO 7176-6:2001 standard.After ensuring that the electric driving system reached a typical working condition, the wheelchair was driven forward to achieve the maximum speed and the speed was recorded.The maximum speed was measured five times and an average speed of 6.3 km/h was obtained, which is shown in Figure 11.In general, the maximum speed of electric wheelchairs is 10 km/h or more, but the developed PAD is for the elderly and disabled, and the maximum speed is set at 6 km/h in consideration of the strength of various manual wheelchair frames and the safety of users.To test the operational characteristics of the developed PAD, a driving operation was conducted on a 10.5° slope, as shown in Figure 10.It was confirmed that the driving torque of the electric assist device was sufficient for a user weighing 100 kg to easily drive up the slope.The maximum slope that the wheelchair could ascend was 20%.The maximum speed test for a manual wheelchair with the PAD installed was performed on a horizontal surface using the ISO 7176-6:2001 standard.After ensuring that the electric driving system reached a typical working condition, the wheelchair was driven forward to achieve the maximum speed and the speed was recorded.The maximum speed was measured five times and an average speed of 6.3 km/h was obtained, which is shown in Figure 11.In general, the maximum speed of electric wheelchairs is 10 km/h or more, but the developed PAD is for the elderly and disabled, and the maximum speed is set at 6 km/h in consideration of the strength of various manual wheelchair frames and the safety of users.A current consumption test was performed on a square test track with a side of 15 m to predict the traveled distance.After the PAD was sufficiently warmed before the test, the current was measured after moving three turns clockwise, and three turns counterclockwise on the test track.The total distance traveled by the wheelchair in one test was 360 m, and the test was conducted thrice.The results obtained were 0.331, 0.367, and 0.377 Ah, and the average was 0.358 Ah.Because the capacity of the battery was above 23.4Ah, the distance that the wheelchair can travel was estimated to be approximately 22.5 km.

Discussions
In Section 2, the new design method for a cycloidal gear was explained, and in Section 3, the designed cycloidal gear was fabricated and installed on a manual wheelchair, and a performance test was conducted to confirm the possibility of using it as a PAD.In several previous studies on cycloid teeth, the profile of the gear was determined according to the diameter of the cycloidal pin roller and the distance from the center of the reducer to its center.However, the cycloidal gear design method proposed in this study can design a different tooth profile while maintaining the size of the cycloidal gear by changing only the TTR in the range of 0.4 to 0.6.This design method can determine the size of the gear by the module and number of teeth, and in particular, if the tooth width ratio is 0.5, it can have a tooth profile very similar to the involute tooth profile.
When designing an internal and external involute gear pair with a difference of one in the number of teeth, a large pressure angle (45°) and addendum truncation are required [14,22].In general, as the pressure angle increases, the noise increases and the efficiency decreases, so a reducer with an involute gear has a higher noise than a reducer with a cycloidal gear.In the lab, two types of reducers with involute and cycloidal gear were A current consumption test was performed on a square test track with a side of 15 m to predict the traveled distance.After the PAD was sufficiently warmed before the test, the current was measured after moving three turns clockwise, and three turns counterclockwise on the test track.The total distance traveled by the wheelchair in one test was 360 m, and the test was conducted thrice.The results obtained were 0.331, 0.367, and 0.377 Ah, and the average was 0.358 Ah.Because the capacity of the battery was above 23.4Ah, the distance that the wheelchair can travel was estimated to be approximately 22.5 km.

Discussions
In Section 2, the new design method for a cycloidal gear was explained, and in Section 3, the designed cycloidal gear was fabricated and installed on a manual wheelchair, and a performance test was conducted to confirm the possibility of using it as a PAD.In several previous studies on cycloid teeth, the profile of the gear was determined according to the diameter of the cycloidal pin roller and the distance from the center of the reducer to its center.However, the cycloidal gear design method proposed in this study can design a different tooth profile while maintaining the size of the cycloidal gear by changing only the TTR in the range of 0.4 to 0.6.This design method can determine the size of the gear by the module and number of teeth, and in particular, if the tooth width ratio is 0.5, it can have a tooth profile very similar to the involute tooth profile.
When designing an internal and external involute gear pair with a difference of one in the number of teeth, a large pressure angle (45 • ) and addendum truncation are required [14,22].In general, as the pressure angle increases, the noise increases and the efficiency decreases, so a reducer with an involute gear has a higher noise than a reducer with a cycloidal gear.In the lab, two types of reducers with involute and cycloidal gear were produced.As a result of comparing the noise, the noise in the involute gear was in the range of 65 to 73 dB, and the noise in the cycloidal gear was 58 to 62 dB.
The tooth size of the harmonic drive is smaller than that of the cycloidal gear due to a difference of two in the number of teeth between the housing gear and cycloidal disk, and these teeth are easily damaged by shock load.Also, the planetary reducers require a multi-stage structure to apply to PAD, as a result, the size of the reducer is larger than that of the cycloidal reducer.Due to these characteristics of the cycloidal reducer, it can be easily applied to the PAD.
As the use time of the cycloidal reducer with pin roller increases, the possibility of vibration due to wear of the pin roller shaft increases [23].However, this problem does not appear in the cycloidal gear proposed in this study because the housing gear and cycloidal disk are directly engaged.In addition, since the housing gear and cycloidal disk have a single contact structure, assembly and clearance management are easy.
PADs should enable a user to move a manual wheelchair and should be user-friendly for inexperienced users.To satisfy these requirements, we proposed an assist device for which a small-sized reducer and a thin cycloidal reducer are required.The joystick was adopted as a wheelchair controller because of its prolonged use in wheelchairs, and it is easy to use and learn.Existing cycloidal reducers are expensive and unsuitable for wheelchairs; therefore, we developed a reducer that has a simple structure and requires a small number of parts to manufacture.This design lowers the production cost of the cycloidal reducer and improves its ease of assembly.
The proposed reducer can be mounted on any manual wheelchair because of its thinness and small size, and it can provide convenience for active users who travel long distances.The manual wheel can be easily released from the power unit by pressing a button at the end of the shaft, allowing the wheelchair to be loaded into a vehicle.The maximum speed of the PAD was set considering the rigidity of the wheelchair frame and user safety.When the maximum speed is exceeded, the wheelchair frame may be damaged by impact with the ground or other obstacles, and there is a risk of tipping when the wheelchair turns rapidly at a high speed.
PADs must have sufficient distance to travel after fully charging the battery to support the daily activities of the user.A larger battery can travel a longer distance, however the weight increases; therefore, the best compromise between travel distance and battery weight is required.Based on the current consumption test results conducted in this study, it is important to determine the optimal battery capacity by measuring the average distance traveled by the user.Additional research is required to reduce the current consumption of the PAD by increasing the efficiency of the motor and reducer.
The developed PAD is fixed to the wheelchair frame through a connector and can act on both folding and rigid frames.The PAD is connected with a connector slightly rearward from the position where the existing manual wheel was, but the PAD is installed while being careful about the movable range of the back and the interference of other members.When the PAD moves backward, the wheelbase becomes more extended, making it safer, but the turning radius increases when the wheelchair turns, making it difficult to move in narrow places [24].Therefore, there is a need to minimize the backward movement of PADs to be developed in the future.
Although the mounting position differs depending on the shape of the frame, it can be installed without interference from other members and the movable range of the back, such as the reclining motion.The developed PAD can electrify a manual wheelchair by attaching a power unit, battery, and joystick to the manual wheelchair.The PAD prototype is easy to install on a rigid wheelchair frame; however, when installed on a folding frame, it will not fold fully owing to the length of the power unit.In future research, the cycloidal reducer will be integrated with the motor to reduce the length of the power unit and optimize the design, enabling the manual wheelchair to fully fold.

Conclusions
In this study, the following results were obtained.
(1) A cycloidal reducer was designed to develop a PAD that can be used by attaching it to a manual wheelchair.The developed cycloidal reducer does not have a pin wheel, and both housing gear and cycloidal disk are designed in cycloid tooth profile.
The cycloidal gear profile can be designed by module, number of lobes, TTR, and eccentricity.In particular, by changing only the TTR, it was possible to design the various gear profiles with the same gear size.The efficiency of the designed cycloidal reducer was 77-78%, the angular transmission accuracy was 14.39 arc min on average, and the backlash was 3.84 arc min.(2) A cycloidal reducer was installed on a manual wheelchair, and then its potential as a PAD was confirmed through a performance test.The PAD is attached to the manual wheelchair through a connector, and the previously used manual wheel can be used immediately by adding an adapter that can be connected to the PAD.The total weight of the power unit was 2.5 kg, and as a result of the performance test, the maximum speed was 6.3 km/h, the maximum movable distance with full charge was about 22.5 km, and the maximum slope that the wheelchair could ascend was 20%.

Figure 7 .
Figure 7. Vibratory forces at the center of the reducer at a maximum speed (_: x-axis direction, _ y-axis direction).

Figure 7 .
Figure 7. Vibratory forces at the center of the reducer at a maximum speed (_: x-axis direction, _ y-axis direction).

Figure 7 .
Figure 7. Vibratory forces at the center of the reducer at a maximum speed (_X: x-axis direction, _Y: y-axis direction).

Figure 9 .
Figure 9. Composition of the power-assist device.

Figure 9 .
Figure 9. Composition of the power-assist device.

Figure 10 .
Figure 10.Slope climbing test for the wheelchair.

Figure 10 .
Figure 10.Slope climbing test for the wheelchair.

15 Figure 11 .
Figure 11.Maximum speed test and consumption test of the wheelchair.

Figure 11 .
Figure 11.Maximum speed test and consumption test of the wheelchair.

Table 1 .
Parameters used in the dynamic simulations.

Table 1 .
Parameters used in the dynamic simulations.

Table 2 .
Results of the designed cycloidal reducer.

Table 3 .
Performance test results of cycloidal reducer.