I am sharing a Matlab code to get a vertex angle from three points.
This is the code, and you can download this one from here <Download>
function [ang] = get_vertex_ang_from_three_points(p0,p1,p2)
% get the vertex angle at p0 from three points p0,p1,p2 % p0, p1,p2 are two dim vector % %%% example % p0=[0;0];p1=[1;0];p2=[0;1]; % get_vertex_ang_from_three_points(p0,p1,p2) % answer = 1.57 (45 deg) %%%
v1 = p1-p0; v2 = p2-p0; ang = acos(v1′v2/(norm(v1)norm(v2)));
It is very easy to use. you can get the vertex angle from three points, It is written in Matlab code
In this post, I will explain how to derive a dynamic equation with Lagrange Equation by MATLAB with Examples. As an example, I will derive a dynamic model of a three-DOF arm manipulator (or triple pendulum). Of course you may get a dynamic model for a two-DOF arm manipulator by simply removing several lines. I am attaching demo codes for both two and three DOF arm manipulators.
If you know all theories and necessary skills and if you just want source code, you can just download from here.
In the attached file, “Symb_Development_3DOF.m” generates a dynamic model. “main_sim_three_dof_arm.m” runs a simulation. You may get a result like this.
1. Example system
Let’s suppose a three DOF arm manipulator shown in the below figure. I am assuming all of masses (M1, M2, M3) exist at the end of links for simplicity. Three actuators exist at each joint, and directly actuate the torques (u1,u2,u3). The manipulator kinematics is governed by three joint angles (q1, q2, q3).
three DOF arm manipulator
2. Theoretical Background
We will get a dynamic equation of this system by using Lagrangian mechanics. If you do not have a background knowledge of Lagrangian mechanics, please refer here.
The general dynamic equation is obtained by
Where, T is the total kinetic energy, V is the total potential energy of the system. where is the generalized force, t is time, is the generalized coordinates, is the generalized velocity. For the example of three-DOF arm manipulator problem, is the torque at the j-th joint, is the angle of the j-th joint, is the angular velocity of the j-th joint.
3. Using Matlab symbolic toolbox
First, let’s define the symbols.
I am using x to represent q, xd for , xdd for L is the length of each link. u is the torque of each joint. g is the gravity constant.
I am sharing the minimal C++ class for Maxon EPOS2. It includes a basic “initialization”, “Move”, “Read position”, “Close device” functions. The program consists of a class called “cmaxonmotor”. You can download the class and demo program here
using namespace std;
int main(int argc, char *argv)
motor.initializeDevice(); // initialize EPOS2
long TargetPosition = -200000;
int CurrentPosition = 0;
motor.Move(TargetPosition); // move to the target position
cout << "Press <Enter> to stop and quit..." << endl;
motor.GetCurrentPosition(CurrentPosition); // get the current position
cout << "Current Position: " << CurrentPosition << endl;
motor.closeDevice(); // close EPOS2
You can control one motor just via USB, and also able to control multiple motors via USB-CAN gateway. For this version, see this article.