Critical Analysis Of Preliminary And Detailed Design And Production Phases For Bicycle Balancing System

Passive Balance Systems

The problem of bicycle balancing is analogous to the known ‘inverted pendulum’ difficulty. In inverted pendulum, the mass is positioned above the pivot

A pendulum can be any elongated object starting from simple rods and mass to a complex system, say a bicycle. A normal pendulum exhibits a stable feature whereas an inverted pendulum exhibits an unstable feature. The main type of motion that is in focus is the ability to stabilize the tilt angle at the contact point with the ground level being relative to the gravity direction [2].

Passive Balance Systems.

Gyrowheel

Gyrowheel is quite novels in implementing passive stabilization in bicycles. Gyrowheel wheel entails the bicycle’s front wheel being replaced by a patented wheel that is made of the embedded flywheel that is gyroscopic and a battery. In accordance with the data collected on the Gyrowheel, a relationship from the tilting angle and rate of balancing (error sensing) provided the data below in graphical form;  

The stability is therefore attained as the motion in tilt is dumped from the vertical axis. Gyrowheel has many strengths like they are easy to install on bicycles. These wheels come with various stability settings. The wheels dampen tilt motion thereby increasing the reaction time of the rider [5].

These wheels have many advantages such being inexpensive, provision of acceptable stability and ease of installation. Also, the wheels do not need power for operation. However, they make the user more dependent on them for balancing and lack provision of stability in all normal conditions in that if the rider’s center of gravity exceeds the width of the polygon then toppling occurs [6].

This active balance system uses a single wheeled system of statistical instability but with dynamical stability properties. The system exhibits non-holonomic features due to the absence of sideways movement. Its entire system is put within the wheel serving as a chasing for the same system. Its control has 3 motors in place. One spins the flywheel to develop dynamic stability, the second rotates the flywheel to control the chassis’ tilt angle and the third drives the chassis.

Data on the Gyrover were taken, giving concentration on the following key parameters. This parameter was used in a simulation then compared with actual experimental results. 

Taking the data of the prototype Gyrover and comparing them to the Extended Kalman Filter produced the graph below. Prototype data came from the input-output information form the Gyrover. This explains the Gyrover balancing technique when compared to the theoretical simulated equation.

The Defense Advanced Research Projects Agency developed this autonomous motorcycle that is riderless. This motorcycle uses the existing video imaging stereo processing together with the GPS navigation in its movement to retain an upright position. In the process 6 gyroscope axis are used to provide its orientation and calculate the angular velocity.  Its degree of turning is very small that it does not inhibit the motorcycles ability to successfully navigate. However, the motorcycle weaves as it moves forward due to the stabilizing nature in a radius of turns that balance its movement [8]

Data collection

The section at hand takes one through the developmental progression of the major designs in this projected system together with the methodology used in implementing an actuated system arm support. There is a detailed information the different subsystems and the integration in the completion of the mentioned design [10].

This flywheel gets its power from a DC motor in that it rotates around the central axis that is orthogonal to the flywheel’s plane. The gimbal is designed for being mounted in a position making its spin axis to freely rotate around a known vertical axis also the motion of rotation around the axis that remains is to be restricted. The rotation around the bicycle’s vertical axis is to be actuated using another DC motor with the configuration indicated below [11]; 

Hence, there comes the mathematical analysis describing how bicycle stabilization is attained using a flywheel. Gyroscopic torque about the bicycle’s roll axis is given by;

It represents the moment of inertia in the flywheel when spinning on its axis. W representing h=the angular velocity exhibited by the flywheel when in the spin axis. What remains in the equation is the angular velocity exhibited by the flywheel when in the vertical axis. The moment causing the tilt in the bicycle comes from gravity; 

W is the bicycle’s weight whereas h is the height representing its center of gravity and theta comes in to represent the tilt angle.  

Here, Its represents he bicycle’s moment of inertia in its roll axis [12].

The design entails 2 actuated support arms behind the bicycle’s seat. More is its lateral offset setting it from the bicycle as below? 

A tilting bicycle on a side makes one arm touch the ground while the other forms an acute angle. The bicycle is forced to maintain the one arm in contact with the ground. This is so until the bicycle is better positioned upright. The stability is better explained when a body’ center of gravity is above the polygon [13].

The bicycle’s tilt angle together with the arm’s angle is explained as below taking the-the bicycle is put on a level surface; 

Where H is the motor’s height of the duration when the bicycle is in an upright position, D representing the measure of distance between the bicycle and the motor. L is the length of the arm, phase is the bicycle’s tilt angle in comparison to the vertical axis

In determining theta, we use the below equation?  

 The simple first strategy in balancing the bicycle entails actuating the cars that can maintain their contact with the ground not considering the tilt angle. The accomplishment is possible by the equation’ 

That produces the desired motor position taking note of the inclinometers values. All these values that entail making contact with the ground have to use the equation in balancing as it provides a relationship between the tilt angle to the ground and provides the system with data having the ground’s location relative to itself [15].

Balancing tilt at threshold whether positive or in a negative direction is the next strategy. Tilt threshold makes use of calculated motor position that has to be with the legs not making contact with the ground during vertical position. The inclinometer makes detections on the tilt angle that are equal or greater than the threshold. The arms then rotate at a constant speed towards a vertical position making the bicycle balance, later the arms move to a general position [2].

Gyrowheel

The desired leg position is determined at a required small constant that is higher than the one calculated in tilt angle threshold correction. The motor position, therefore, has to be above the ground. The movement and speed of the motor are limited so that the motor moves from the initial position to the desired position.

The weight and the strength of this bicycle balancing system are the constraints for realizing its design. Another matter is the cost of the materials that were influenced by the final decisions. These constraints influenced the design choices that were easily present to be able to make the design [4].

Arm actuation requires high torque and low rpm motors. These arms should also move independently and two motors are needed. The motors chosen were 2 12V motors that spin at 96 rpm when not loaded and can develop 325 in lbs. torque. Arms, sprockets and chains, pulleys and timing belts or the direct drive had several options had to be cheaper, readily available and have a high accuracy. The compensation the lack of accuracy there was a PID loop in control that determined the actual arm position [5].

The microprocessor PIC32MX460F512L handled the overall system. It has 32-bit processing designed to run at 80 MHz in embedded systems.

The used approach was the bottom-up technique. The software had to directly interface with the used PIC32’s making use of the macros like ADC1CHSbits.CHOSA. The channel select bits.

Separate sensors- they were the MEMS accelerometer together with the solid-state gyroscope that investigated the effective tilt angle detection. The sensor used was an Inertial Measurement Unit (IMU). The circuit board had two separate sensors. Though they can together detect motions in 5 degrees of freedom their quality is not high enough for detection.

Single sensor accelerometer – a single axis UITS-2B manufactured inclinometer was used. This sensor output analog DC voltage that has to be shifted down to match the PIC32’S range of operation. The attenuated voltage can then be sampled using ADC of the PIC32 processor to determine the required position of actuated arms. It is more accurate than IMU.

The electrical components vary in power and the required IO voltage. A design for the compliance of these electrical components was done and the design involved hardware and actuators with the operating system having analog signal sensors followed by processing of data as illustrated below [7].

There is need to use circuits that condition the signals in non-compliant components using interfacing points. An attenuation circuit is used in the output pin of the inclinometer giving out 0-5 volts of the analog signal. The attenuation circuit also has to have a linear relationship between the input and the output signals to prevent distortion.  A voltage divider with gain 2/3 is used in this case.

Amplification is also key between the processor digital output pins. The final circuit diagram is shown below [12];

The resulting data was produced from a PIC32 interface that consisted of sensor input and the motor control signal data. The figure below shows the general overview of the desired prototype that is attached to a bicycle. The arms rest the PID control loo. Using short arms prevent damage of the stem in case there was a malfunction in the control of the PID.

A production of a close view of the subsystem’s actuation is also shown below. In also shows how the arm drives the wired potentiometer using the timing belt.

A total of experiments were done to provide a validation of the system. The first experiment determining how well the system can detect the bicycle’s angle of tilt and calculate the required arm position that maintains contact with the ground. This was made possible by the disconnection of the chain between a support line and a drive motor thus making the arm rotate freely with arm’s end maintaining contact with the ground with the effect of gravity. Data were obtained from the potentiometer reading in bits and sampled at a rate of 388.2 samples in a second

There is an 84% error data magnitude to 10 bits or less corresponding to a difference of 2.4⁰ measure arm position by the potentiometer and the calculated data by the inclinometer.

The second experiment investigated the PID control loop arm actuation to the desired overall position. The arm got attached to the motor drive completing a closed-loop feedback. Data from the inclinometer output, potentiometer reading, and desired potentiometer were obtained and sampled wit rate 388.2 Hz in the duration of 10 seconds. The desired and actual position of the arm position in time is shown below [15];

It was noted that 62.8% of the time, the actual arm position was in 2.4⁰ desired position. 88.5% the arm was in 3.6⁰ in the desired position and 97% it had 4.8⁰ of position. The result was very satisfying though there could be room for improvement.

Conclusion

The balancing designed used active assistance in the integrated system to make use of the electrical and mechanical hardware together with the software to balance the bicycle. The information obtained during the operation of the project provided validation that this system has been modeled properly for the control of the closed loop PID. The system marketable prototype produced an envisioned easily attachable to any standard bicycle of any given size. The project is believed to be useful in learning tools and can be used by disabled or an injured person to ride a bicycle who could fail to ride a bicycle otherwise [5].

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