The last step is to equalize the linear velocity vector of the standard wheel to that of equation 3. ( ■(s(α+β)&-c(α+β)&-cβd@c(α+β)&s(α+β)&sβd@0&0&0) )( ■(x ̇@y ̇@θ ̇ ) )=( ■(rψ ̇@0@0) ) (4)
In case of the steerable standard wheel, equation 4 can be used in the same way, if the fixed angle β is replaced by a function β(t). This equation could also be applied to the spherical wheel (because of the forces which affect the wheel and change β(t), only a linear velocity in the rolling direction exists). If the wheel is a castor wheel, the y-component of the velocity vector is depending on the angular velocity β ̇ and the length of the rod (see equation 5). ( ■(s(α+β)&-c(α+β)&-cβd@c(α+β)&s(α+β)&sβd@0&0&0) )( ■(x ̇@y ̇@θ ̇ ) )=( ■(rψ ̇@-d_c β
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The vector q ⃗ describes the configuration (position and orientation) of the robot at any time. q ⃗=[■(x&y&ϕ)]^T (7) where x, y are the coordinates of the robot (point o) in the inertial frame. If the linear speed and angular velocity of the robot are v and ω, respectively, assuming no-slip on the wheels, the velocity components can be written as x ̇=v cosϕ (8) y ̇=v sinϕ (9) ϕ ̇=ω (10)
The kinematics of motion of the robot can be written as follows: q ⃗ ̇= [■(cosϕ&0@sinϕ&0@0&1)] u ⃗ (11)
Where, q ̇ is the time derivative of configuration q and u ⃗=[■(v&w)]^T is the control input given to the robot for navigation. The angular and linear velocity of the robot can be written in terms of the linear velocities of the right and the left wheel centers (v_r,v_l) ω=(v_r-v_l)/2d (12) v=(v_r+v_l)/2 (13)
Here for the right wheel, the Newton-Euler equation is expressed as F_r - f_r = m_w x ̈_r (14) τ_r - F_r .r = J_w ω ̇_r (15) where F_r is the reaction force applied to the right wheel by the rest of the robot; f_r is the friction force between the right wheel and the ground; m_w is the mass of the wheel; τ_r is the torque acting on the right wheel provided by the right motor; r is the radius of the wheel; and J_w is the inertia of the wheel. Note that the Coriolis part had been deleted since it is negligible due to the fact that the wheel inertia is much smaller than the robot inertia.
Similarly, for the left wheel we can write F_l - f_l = m_w
A trip consisted of one revolution. Six stops were made for loading and then one, nine minute, nonstop revolution. The fare for the trip was 50 cents. Ferris and his wife were the first to ride it along with the city’s mayor and a 40 piece band. The wheel was a huge success. It earned $726, 805 and $395,000 in profit. Several couples were married at the top of the wheel because of its beauty and fame. 3000 light bulbs were on the wheel to create a beautiful sight as they blinked. The wheel made 10,000 revolutions and carried 1.5 million passengers. The wheels last days were nearing. It ran smoothly until November 6, 1893, when the exposition ended. $400,000 in new debt and investors sold the structure for $1,800. It was reassembled in ST Louisiana for the Louisiana Purchase Exposition. Three million new riders enjoyed the wheel. The exposition soon closed because of complaints that the wheel was an eyesore. After the exposition, the wheel was moved to Chicago. Residents there petitioned to have the wheel removed. They stated that it was useless and undesirable. On May 11, 1906, 200 lbs. of dynamite reduced the wheel to a pile of scrap metal.
Next, there is a while loop that continues to run if the left encoder is less than the value of the number of revolutions multiplied by the counted ticks per revolution. After this, if the computed motor ticks are unequal between the two motors, the function is written to where the vehicle can adjust and correct itself if it starts to drift to one side. This is done by if-else statements in which each motor power is adjusted. Variables used in the driveStraight() function were used in the turnLeft () function as well. The function contains a turningTime variable, which is set to the inputted angle multiplied by 1000 and is divided by the inputted turning speed. Like the previous function, if-else statements were used to adjust each of the motors power to make a proper turning angle. At the end of the function, the command encoder.clearEnc(Both) clears both the encoders counted motor
The two types of friction of the mousetrap car are rolling friction and static friction are the two types of friction that may affect the performance of the mousetrap car. The problem of the friction did I encounter and how do you solve them one types of friction i encounter was the static friction I had to take off some glue from the stick that had my wheels and to open eye screws. The factor did take into account to decide the number of wheels you decide to chose for the mousetrap car I saw a video of a car that had 4 wheels and it ran really fast, so I thought a 4 wheeled car would run fast or at least the four meters. What kind of wheels did I use in each axles I use tires as my wheels on each axles. I think the affects on using big wheels
The equivalent electrical circuit of a dc motor is shown in figure 5.2. It can be represented by a voltage source (Va) across the coil of the armature. The electrical equivalent of the armature coil can be described by an inductance (La) in series with a resistance (Ra) in series with an induced voltage (Vc) which
Using Vernier, we clicked collect while releasing the cart after motion detector starts to click. This was done moving the hand quickly out the path. Using logger pro, indicated which portion was to be used by dragging across the graph to indicate the starting and ending times. Then the linear button was clicked to perform the linear regression of the selected data. The Linear Button was used to determine the slope of the velocity vs. time graph, only using the portion of the data for times when the cart was freely rolling. We found the acceleration of the cart from the fitted line. Record the value in the data table. These steps where repeated 5 mores times. Measured the length of the incline, x which is the distance between the two points of the ramp. Measure the height, h, the height of the book(s). The last two measurements was used determine the angle of the incline. Raise the incline by placing a second book under the end. Adjust the book so that distance, x, is the same as the previous reading. Repeated these steps with 3, 4 and 5 books.
In the most common form of 1-DOF torsional plant, friction is taken as being viscous. Applying Newton's second law to the attached rotating disk using free body diagram method then following up with differential equation and the deducing:
The car, being above the ground, has gravitational potential energy. Which, when placed on the ramp, transforms into kinetic energy. This kinetic energy pushes the car down the ramp, towards the ground and the momentum carries the car forward. The wheels allow it to gain more distance, as using wheels is the most effective way of transporting something. Having only 3 groups of wheels reduces friction compared to having 4 groups of wheels.
The leaping in the first revolution _{1u} is given by ((tR_{u})/2)-0 and the leaping in _{2u} is given by (((t+2)R_{u})/2)-((tR_{u})/2). Furthermore, the leaping in _{um_{u}} is given by ((R_{u}(t+m_{u}))/2)-((R_{u}(t+(m_{u}-1)))/2). Then, the distance L_{u} is given by:
The device that displayed the best motion had three wheels. The reason that the device with three wheels displayed the best motion might have been due to the fact that it was the most secure out of the two. The device was much more even than the device with four wheels, holding the front tire in place and making sure it did not add more mass to one side than the other. The device with four wheels had multiple instances where the front tires would lean more to one side than the other. The average distance the three-wheeled device traveled was 888 cm while the four-wheeled device traveled 486 cm, a 402 cm difference between the averages.
This provides the kart with centripetal force required for circular motion. Without centripetal force, go karts will not be able to turn corners. The equation Fc=mv2/r is used to calculate how much centripetal force is acting on an object(in this case a gokart) when turning a corner, from this equation we are able to see relationship between velocity and radius. If the velocity of the kart increases, the centripetal force required to make a turn of equal radius also increases. If the radius of the corner is large, the centripetal force required to turn the corner decreases as it is easier to turn vise versa.
Thus we have the equation of the pendulum’s linear motion Lθ” + 2L’θ’+ gθ = 0(3) Lθ and (Lθ)’ represent the pendulum’s sweep (fig.4) and curvilinear velocity,
Ubiquitous tire manufacturer Goodyear is apparently trying to make the spherical tire go from science fiction to a reality. With the introduction of more driverless vehicles, Goodyear will introduce
A rightward moving rider gradually becomes an upward moving rider, then a leftward moving rider, then a downward moving rider, before finally becoming a rightward-moving rider once again. There is a continuing change in the direction of the rider as he/she will moves through the clothoid loop. A change in direction is one thing of an accelerating object. The rider also changes speed. As the rider begins to climb upward the loop, he/she begins to slow down. What we talked about suggests that an increase in height results in a decrease in kinetic energy and speed and a decrease in height results in an increase in kinetic energy and speed. So the rider experiences the greatest speeds at the bottom of the loop. The change in speed as the rider moves through the loop is the second part of acceleration which the riders experiences. A rider who moves through a circular loop with a constant speed, the acceleration is centripetal and towards the center of the circle. In this case of a rider moving through a noncircular loop at non-constant speed, the acceleration of the rider has two components. There is a component which is directed towards the center of the circle (ac) and relates itself to the direction change and the other component is directed tangent (at) to the track and relates itself to the car's change in speed. This tangential component would be
Trajectory of a vehicular system can be reconstructed from noisy position data. Smoothing spline is an efficient method of reconstructing smoothing curves. In conventional smoothing spline, the objective function minimizes errors of observed position points with a penalty term, who has a single parameter that controls the smoothness of reconstruction. Adaptive smoothing spline extends single parameter to a function varying in different domains and adapting the change of roughness. In this paper, using Hermite Spline, we
Some basic works have been done in the field of serpentine belt drives are researches on the vibration characteristics of axially moving string. Beikmann et al., (1996) applied a mathematical model to examine the transverse vibration and stability of coupled belt-tensioner systems. Meanwhile, they modeled and analyzed the serpentine belt drive systems with a dynamic tensioner shown as figure 3.1.