Rob2.md

Robotics 2

1. D-H Notation

Step 1: Assign Frames according to the 4 D-H Frame Rules

Step 2: Fill out the D-H Parametric Table

Step 3: Plug the table into the Homogeneous Transformation Matrix formula.

Example 1:

Step 3: Plug the table into the Homogeneous Transformation Matrix formula.

Step 4: Multiply the matrices together

2. Forward Kinemtics

Example:

Any of the 2 processes, it will still arrive on the same answer.

Determining the position and direction using Forward Kinematics.

Simulation and visualization of Forward Kinematics using MATLAB:

If θ1=0֯ and θ2=0֯:

If θ1=90֯ and θ2=-90֯:

If θ1=45֯ and θ2=30֯:

2.1 Forward Kinematics in Python and MATLAB

Codes can also be found from: https://github.com/MikkoDT/Robotics-2-2022-2023 And the tutorial for installation of Robotics Toolbox by Peter Corke in Python can be found here: https://youtube.com/playlist?list=PLUgsbeZHs9qMFXTIQPW0clLoRkf_oiBoX&si=0sYu2QIJ4NWilTq7

spartankit_test.py of 3-DOF SPARTAN Robotkit

Project code

MATLAB of 3-DOF SPARTAN Robotkit

Project code

4. Spherical Wrists

SCARA PRR Variant 3

3-DOF

6-DOF

5. Inverse Kinematics

Graphical Method for Solving Inverse Kinematics

• Example:

5.1 Inverse Kinematics of Cartesian Manipulator

5.2 Inverse Kinematics of Articulated Manipulator

5.3 Inverse Kinematics in Python

Codes can also be found from: https://github.com/MikkoDT/Robotics-2-2022-2023

IKin.py of SCARA-V3

Inverse Kinematics of SCARA-V3

import numpy as np

link lengths in mm

a1 = float(input("a1 = "))

a2 = float(input("a2 = "))

a3 = float(input("a3 = "))

a4 = float(input("a4 = "))

Position Vector in mm

x0_3 = float(input("x0_3 = "))

y0_3 = float(input("y0_3 = "))

z0_3 = float(input("z0_3 = "))

Inverse Kinematic Solutions using Graphical Method

Solution 1

phi2 = np.arctan(y0_3 / x0_3)

phi2 = phi2 * 180 / np.pi

Solution 2

r1 = np.sqrt((y0_32) + (x0_32))

Solution 3

phi1 = np.arccos((a42 - r12 - a2**2)/(-2 * r1 * a2))

phi1 = phi1*180 / np.pi

Solution 4

theta2 = phi2 - phi1

solution 5

phi3 = np.arccos((r12 - a22 - a4**2)/(-2 * a2 * a4))

phi3 = phi3 * 180 / np.pi

Solution 6

theta3 = 180 - phi3

Solution 7

d1 = z0_3 - a1 - a3

Displaying the Joint Variables

print("d1 = ", np.around(d1,3))

print("theta2 = ", np.around(theta2,3))

print("theta3 = ", np.around(theta3,3))