Inverse kinematics is a metodic used to determinate the joint angles of a robotic arm based on a desired position of its end effector. In a 3 decrees of freedom (3DOF) system, calculating these angles engeometric and trigonometric principles. This article provides a step- by- step guide to perfoming these calculationes.

Understanding thee Robot Configuration

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

Step 1: Určete si cíl Position

Identifify thee desired position of thee end effector, represented by coordinates (x, y, z). These coordinates serve as thes basis for calculating thee joint angles.

Step 2: Calculate te Base Joint Angle (θ1)

Te firtt joint angle, θ1, is typically the rotation around the vertical axis. It can bee calculated using thee projection of thee gate position onto tho te XY- plane:

CLANE1; CLANE1; FLT: 0 CLANE3; CLANE3; θ1 = atan2 (y, x) CLANE1; CLANE1; CLANE1; CLANE3; CLANE3; CLANE3;

Step 3: Calculate te Writt Position

Odsuňte to, co je důležité, protože to je to, co je důležité, aby to bylo pozitivní.

CLAS1; CLAS1; CLAS3; CLAS3; r = sqrt (x ² + y ²) - link1 _ length CLAS1; CLAS1; CLAS1; CLAS3; CLAS3c;

a to je vertikal distance:

CLAS1; CLAS1; CLAS3; CLAS3; s = z - link0 _ height CLAS1; CLAS1; CLAS1; CLAS3; CLAS33;

Step 4: Calculate thee Elbow and Shoulder Angles

Using the Law of Cosines, compute the angles at the elbow and shouldder joints. Define:

  • CLAS1; CLAS1; FLT: 0 CLAS3; CLAS3; D = (r ² + s ² - link2 _ length ² - link3 _ length ²) / (2 * link2 _ length * link3 _ length) CLAS1; CLAS1; FLT: 1 CLAS3; CLAS3;

- Ne, ne, ne.

CLAS1; CLAS1; FLT: 0 CLAS3; CLAS3; θ3 = ACO (D) CLAS1; CLAS1; CLAS1; CLAS3; CLAS3c;

A to by mělo být dobré.

CLAS1; CLAS1; CLAS3; CLAS3; θ2 = atan2 (s, r) - atan2 (link3 _ length * sin (θ3), link2 _ length + link3 _ length * cos (θ3))

Step 5: Finalize te Joint Angles

Konvertovat all calculated angles to degrees if necessary. Ověření, že angles are s in te robot 's joint limits before appliying them.