Kinmatics program

Enrolled in a mechanical physics class? This calculator program for the TI Plus CE will make calculations easier and quicker with automatic solvers for the kinematic equations! The program allows you to choose which of the three equations to use, input your values, select an unknown value, and it calculates the rest for you. Continue reading for a walk-through of how to create the program yourself, or press the button below to jump directly to the finished code.

To create a program, press the prgm button and scroll over to NEW. In order to select an unknown variable, we first need to create a placeholder variable to type at the desired location. We do this by assigning a random number to X. Next, create a selection menu using the menu command found by pressing prgm and scrolling down.

The first string is the title of the menu, followed by the name of each option and a label variable. Use the letters A-D as label variables and create options for the three equations and an option to quit. We can easily complete the quit option by designating the start of label D Lbl found pressing prgm and scrolling down and telling the program to Stop same location as Lbl. The rest of the program is fairly simple as long as you keep track of the variables and what they represent. You can design all of the mechanisms in a machine at the same time so that you can see all of the important mechanism interactions.

You can even add the packaging to the model and design it as a mechanism. Motion Design is integrated with MechDesigner as a standalone tool - which we call it MotionDeisgner. MotionDesigner is a powerful motion design editor. You can edit and simultaneously update the motions to the mechanism design and cam design in your MechDesigner model - on-the-fly. In this way, you can scrutinize your motion design as a graph in MotionDesigner, and simultaneously scrutinize the same motion moving in your MechDesigner model of your machine.

You can design, any mechanism using Inverse-Kinematics or Forward-Kinematics. MechDesigner has fast, closed-form algorithms, you will be amazed at how quickly you can innovate and watch a simulation cycling at machine-like speeds. Start your free day trial today. This piece of code performs inverse kinematics using the pseudoinverse of the Jacobian. What does that mean? Let me explain now how this process works. You start off with the joints of the robotic arm at arbitrary angles by convention I typically set them to 0 degrees.

Calculate the distance between the current end effector position and the desired goal end effector position. Reduce the delta p vector by some scaling factor so that it is really small. We only want the end effector to move by a small amount at each time step because, for small motions, we can approximate the displacement of the end effector as linear. Doing this makes the math easier, enabling us to use the Jacobian matrix.

The Jacobian matrix is, at its core, is a matrix of partial derivatives. Remember, forward kinematics i. The pseudoinverse of the Jacobian matrix is calculated because the regular inverse i.

J -1 which we looked at in a previous tutorial fails if a matrix is not square i. The pseudoinverse can invert a non-square matrix. Multiply the pseudoinverse of the Jacobian matrix and the scaled delta p vector together to calculate the desired tiny change in the joint values. The resulting motion from updating the joint values should bring the end effector just a little bit closer to your desired goal position. In a nutshell, at each iteration, we have the end effector take tiny steps towards the goal.

We only stop when the end effector reaches the goal position. Once the end effector is close enough, return the final joint angles. For a real robotic arm, these are the angles that each servo motor would need to be for the end effector of the arm to be at the goal position.

In this piece of code, we calculate the Jacobian matrix position part on the top half…not the orientation part on the bottom half. For a revolute joint like a servo motor , the change in the linear velocity of the end effector is the cross product of the axis of revolution k which is made up of 3 elements, k x , k y , and k z and a 3-element position vector from the joint to the end effector.

For example, given a robotic arm with two joints i. My email is swailsey msn. I hope this program comes in handy, but a tip is to use it to check your answers rather than become dependant on it as a source of them.

Physics Set v3. It is very useful for the average Honors Physics student. Now incorporates a new GUI for two programs, and increases efficiency. Physics Solves for freefall, kinematics, and centripital force. Phyzics New and improved!

This new version of Phyzics can hold up to equations, with the ability to type in an equation to solve only once or to save for later use! Functionality is much improved and the interface is easier. Newest release: includes minor changes to allow for better storing and accessing capabilities for user-defined equations. This version: big bug fix over v1. I apologize for having to rerelease so soon. Motion in a Plane with Constant Acceleration This is a generalization of my program, Projctle , to include acceleration due to forces other than gravity.

For example, it can be used for a charged particle moving in a uniform electric field. Try it out. Projectile Motion This update of projctle allows entry of either initial or final values, or any combination of initial and final values, and also removes the restriction that the projectile start at 0,0. The previous version of projctle required initial values as input and calculated final values.

Projctle solves most types of projectile motion problems, assuming no resistive forces. Choose from 3 different systems of units. Solutions are copied to the home screen. The program solves most types of projectile motion problems. The solutions are copied to the home screen. The path of the projectile and the path in vacuum are graphed for comparison.

After exiting the program, the graphs can be examined and input values can be changed. Protect Finds almost anything about a projectile. Then, it can find where on a building it will hit. Displays a rough graph, too! Check out your graph mode to see the real graph. Pushing an Item on Incline I wrote this program after finding myself trying to push a car from rolling down a driveway. Enter the angle of the incline, mass of the object, and the coefficient of friction, and calculate the minimum applied force needed to prevent the object from accelerating down.

Enter the values with the parameters of pushincl angle, mass, coefficient. Range Formula Solver Solves the range formula for range, initial velocity, angle, or gravity. Sections v 1. Simple Harmonic Motion Analyzer Given values for 4 of 10 parameters, this program returns values for all relevant quantities in simple harmonic motion, including energy, amplitude, period, frequency, mass, force constant, initial position and velocity, angular frequency, and phase constant. It also returns equations for position, velocity, and acceleration as functions of time.

It evaluates position, velocity, and acceleration at a given time, velocity and acceleration at a given position, or the time at a given position.