Roboterarm mit Gewicht — Haltemoment, Regelung, Kopplung (3D)
About this app
Die richtigen Winkel reichen nicht: Ein senkrechter Zwei-Glied-Arm mit Last muss gegen die Schwerkraft halten (Moment = Gewicht × Hebelarm), Trägheit beschleunigen und die Kopplung der Gelenke beherrschen. Sprungantworten mit P und D, derselbe Regler angezogen und ausgestreckt, schlenkernder Unterarm und Computed Torque — echte Dynamik, RK4 in Echtzeit.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
The idea
A robot knows the angles it has to reach, but that does not make the arm stand still. Every motor has to hold against gravity: the holding torque is weight times lever arm, the horizontal distance from the joint to the centre of mass. It is largest with the arm stretched horizontally and zero when it points straight up. On top come inertia, which depends on the pose, and coupling: if the shoulder moves quickly, a torque acts on the elbow. A simple controller that only reacts to the angle error therefore sags or overshoots.
What the app shows
A vertical arm with shoulder, elbow and a load in the gripper stands in a 3D scene. Lever arms, centres of mass, weight forces and motor torques are shown as segments, arrows and torque arcs, and a panel works out the holding torque as the sum m·g·x. The motion is computed in real time from the equation of motion. Four stations lead from holding torques via the step response of a PD controller and the influence of the pose to coupling and a model-based controller (computed torque).
Things to try
Put the arm horizontal and vertical, drag the gripper and switch the motors off: the arm falls. In station 2 try a controller that is too weak, too strong and well damped. In station 3 compare the same step on the folded arm and on the stretched arm with 10 kg. In station 4 swing the shoulder once without and once with a model in the controller.
Frequently asked questions
- How do you calculate the holding torque of a robot arm?
- Each part of the arm and the load produces a torque at the joint equal to its weight m·g times the horizontal distance from the joint to its centre of mass. The sum is the holding torque the motor has to supply. It is largest with the arm stretched horizontally and vanishes when the centre of mass is directly above the joint.
- Why does a robot arm with a P or PD controller sag?
- A P or PD controller produces torque only in proportion to the angle error. To carry the permanent weight, a steady-state error must remain: e = holding torque / K_P. A larger K_P makes it smaller but, without enough damping, makes the arm prone to oscillation. Gravity feed-forward or an integral term (PID) removes it.
- What is computed torque control in robotics?
- Computed torque is a model-based control method: using the equation of motion M(q)q̈ + C(q,q̇)q̇ + g(q) = τ, the controller computes which torque each joint needs for the planned motion, including gravity, pose-dependent inertia and coupling. Feedback then only corrects small model errors.
- What can I try in the “Robot arm with weight” app?
- You set pose and load, see lever arms and holding torques, switch the motors off, run step responses with adjustable stiffness and damping and compare overshoot, settling time and steady-state error. The controller can compensate nothing, the weight, or weight and momentum. The model is a two-joint teaching model.
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
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