Robot Arm Simulator for Kinematics and ROS Planning

Controls

The simulator provides joint sliders, a draggable tool target, frame overlays, and link-dimension controls, with the base centred so the full 360° reachable workspace is visible. Forward mode calculates the tool pose from the joint angles you set. Inverse mode tracks a target you drag — solving for joint angles live and reporting unreachable or ambiguous targets rather than silently snapping to a result. A third pick-and-place mode lets you position a pickup point and a destination, then runs the arm through the whole task: it moves to the object, grabs it, carries it, and releases it in the dropzone — the canonical job every real manipulator is built to do.

Theory

Each joint contributes a transformation between coordinate frames. Multiplying those transformations from the base to the tool yields the forward kinematic pose. Inverse kinematics works backward and may have no solution, one solution, or several solutions.

Near a singularity, a small tool motion can demand a very large joint motion. A planner must also respect position, velocity, acceleration, torque, and collision limits. Geometric reach alone does not make a trajectory safe.

Algorithm

1. Define link lengths, joint axes, home transforms, and joint limits.
2. Compute forward kinematics for the current joint state.
3. Compare the current tool pose with the requested target.
4. Use an analytic or numerical solver to reduce pose error within limits.
5. Reject colliding or singular candidates and select a continuous solution.
6. Time-parameterize the path and send synchronized setpoints to joint controllers.

Source code

A planar two-link arm has a compact forward model:

from math import cos, sin

def forward_kinematics(theta_1, theta_2, link_1, link_2):
    elbow = (link_1 * cos(theta_1), link_1 * sin(theta_1))
    tool = (
        elbow[0] + link_2 * cos(theta_1 + theta_2),
        elbow[1] + link_2 * sin(theta_1 + theta_2),
    )
    return elbow, tool

For physical arms, validate every planned trajectory in a bounded, collision-aware environment before enabling actuator power.

Assumptions and hardware differences

The arm is planar with two or three revolute joints, perfectly rigid links, instant velocity response and no gravity, dynamics or collision — you can swing from elbow-up to elbow-down with no torque limit. Real servos have position and velocity limits, gear backlash, current-limited torque and payload-dependent sag, and a 6-axis arm must also manage orientation, singularities and work near joint limits. This lab is where you learn why a target inside the annulus can have two solutions and why a target on its edge is singular, before you add the dynamics that make those poses hard to hold.

Circuit diagram

Separate high-current actuator power from compute power while maintaining the reference and safety signals required by the selected hardware.