Warum ist ein Roboterarm so schwer zu steuern? (3D)
About this app
Ein Tischarm in sechs Stationen: Vorwärts ist eine Formel mit genau einer Antwort, rückwärts schneiden sich zwei Kreise in zwei, einem oder keinem Punkt, mit drei Gliedern gibt es unendlich viele Lösungen. Herantasten Gelenk für Gelenk, eine Säule als Insel auf der Landkarte der Winkel, die sich zum Donut rollt, und die gestreckte Lage, in der das Parallelogramm der Handbewegungen flach wird.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
What it is about
A robot can only set its joint angles directly, but tasks are stated in space. Computing the hand position from the angles (forward kinematics) is a sum of arrows with exactly one answer. The other way round (inverse kinematics) there are none, one, two or infinitely many solutions, often no closed formula, obstacles that look completely different in the space of angles, and singularities in which the hand loses a direction of motion.
What the app shows
A SCARA-like table arm with two links (2 m and 1.5 m) above a drawing board, in six stations. Backwards, the circle around the shoulder and the circle around the target intersect; their intersections are the possible elbows. With three links a fan shows infinitely many solutions. Groping (CCD) turns one joint after another towards the target. A pillar becomes an island on the map of angles (configuration space), and the map rolls into a torus. Finally the columns of the Jacobian span a parallelogram that becomes flat in the stretched pose.
Try it yourself
First try to hit the cup with the two angle sliders only. Then drag the target outwards until the circles no longer intersect. Let the arm grope from two start poses. On the map, compare the direct path that hits the pillar with the planned path, and roll the map into a doughnut. In the last station, move the elbow towards 0° and watch the required joint speeds outwards explode.
Frequently asked questions
- Why is inverse kinematics harder than forward kinematics?
- Forward kinematics plugs joint angles into formulas with sine and cosine and always gives exactly one hand position. Inverse kinematics has to solve these equations for the angles. There may be no solution (target out of reach), several solutions (elbow left or right) or, for redundant arms, infinitely many, and from six axes on usually no simple formula.
- What is the configuration space of a robot arm?
- The configuration space contains every pose of the arm as a single point; with two revolute joints it is a square of angle pairs. Because −180° and 180° are the same pose, opposite edges belong together, so the square is really a torus. Obstacles in space become regions of forbidden poses there, around which a path planner searches.
- What is a singularity of a robot arm?
- At a singularity the hand loses a direction of motion, for instance when the arm is fully stretched. Mathematically the determinant of the Jacobian becomes zero; for the planar two-link arm det J = ℓ₁ℓ₂ sin q₂. Nearby, even slow hand motions demand very high joint speeds.
- What can I try in the app?
- You steer a table arm through six stations: grab a cup, compute forwards, find solutions by intersecting circles, grope with CCD, plan a path around a pillar on the map of angles, and examine the stretched pose. A maths panel shows the formulas with current numbers, and a section “For the curious” links to higher mathematics.
Subject: Engineering mechanics
More from Engineering mechanics
- Bending stress & moment of inertia
- Düsenjet bis v_max (3D)
- Energy & oscillation
- Truss analysis (method of joints)
- Equilibrium & support reactions
- Kinematics
- Kinetics & Newton's second law
- Forces & vector addition
A VisuApp by heyprof: interactive, free in your browser, no sign-up. What is a VisuApp? · All apps