Step-by- step Obliczanie 3dof Inverse Kinematyki

Inverse kinematics is a methode used to determinate thee joint angles of a robotic arm based on a desired position of it end effector. In a 3 degrees of freedem (3DOF) system, calculating these angles involves geometrric and trigonometric principles. Thies articlie provides a step guide to perfoming these calculations.

Understanding the Robot Configuration

Before starting calculations, it is essential to understand thee robot 's structure, including link lengths andd joint type. Typically, a 3DOF robot has three rotational joints, each contriing te te overall position of thee end effector in 3D space.

Krok 1: Określić, że te Target Pozytion

Identyfikacja tych desired position of thee e end effector, consigeted by y coordinates (x, y, z).

Step 2: Calculate the Base Joint Angle (θ1)

Te first t joint angle, θ1, is typically thee rotation around thee vertical axis. It can be cacaliated using thee projection of thee target position onto the XY- plane:

Xi1; Xi1; FLT: 0 Xi3; Xi3; θ1 = atan2 (y, x) Xi1; Xi1; FLT: 1 Xi3; Xi3;

Step 3: Oblicz te Wrist Pozytion

Subtract thee contribution of thee first joint to o thee wrict position, which is thee point when thee lass two joints operate. This involves calculating thee planar distance:

(x ² + y ²) - link1 _ length (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1); (1) (1) (1); (1); (1) (1) (1); (1); (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1

and the vertical distance:

Xiv1; Xiv1; FLT: 0 Xiv3; Xiv3; s = z - link0 _ height Xiv1; Xiv1; FLT: 1 Xiv3; Xiv3;

Step 4: Oblicz te Elbow i Shoulder Angles

Using thee Law of Cosines, compute the angles at thee elbow and should der joints.

Then, thee elbow angle:

Xi1; Xi1; FLT: 0 Xi3; Xi3; θ3 = acos (D) Xi1; Xi1; FLT: 1 Xi3; Xi3;

I że powinno być inaczej:

(s, r) - atan2 (link3 _ length * sin (θ3), link2 _ length + link3 _ length * cos (θ3)))

Step 5: Finalize the Joint Angles

Zamień all calculated angles to degrees if necessary. Verify the angles are e within thee robot 's joint limits before applicying them.