Robot Arm Simulator for Kinematics and ROS Planning
Explore joint limits, forward kinematics, inverse kinematics, and safe motion planning in a browser-based robot arm simulator preview.
- Category
- ROS
- Time
- 3–6 hours
- Platform
- Browser · ROS 2
01 / Start here
Introduction
Robot arms turn joint commands into precise tool motion through geometry, feedback, and planning. This project introduces that chain without hiding the difficult parts. The planned simulator will expose coordinate frames, reachable poses, joint limits, and singularities so ROS users and robotics students can understand why a requested motion succeeds or fails.
Live lab / Planar forward & inverse kinematics
Robot arm simulator
Move the joints to see the tool pose, or set a target and watch inverse kinematics solve for the joint angles — with honest reach, singularity, and limit reporting.
The filled anchor is the base; segments are links with round joints; the tool shows a small x/y frame. In inverse mode the dashed circles are the reachable workspace, the marker is the draggable target, and the faint arm is the other elbow solution.
- Tool X
- 0 px
- Tool Y
- 0 px
- Tool angle
- 0°
- Status
- Reachable
- Reach
- 0 / 240 px
Keyboard: focus the workspace, then use Space to run/pause, N to step, R to reset, B to switch elbow, and F for full screen.
Controls
The planned simulator provides joint sliders, a draggable tool target, frame overlays, link dimensions, and joint-limit controls. Forward mode calculates the tool pose from angles. Inverse mode searches for joint angles and reports unreachable or ambiguous targets rather than silently snapping to a result.
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
- Define link lengths, joint axes, home transforms, and joint limits.
- Compute forward kinematics for the current joint state.
- Compare the current tool pose with the requested target.
- Use an analytic or numerical solver to reduce pose error within limits.
- Reject colliding or singular candidates and select a continuous solution.
- 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, toolFor physical arms, validate every planned trajectory in a bounded, collision-aware environment before enabling actuator power.
Circuit diagram
Separate high-current actuator power from compute power while maintaining the reference and safety signals required by the selected hardware.
Hardware checklist
Components
- Three-axis or greater robot arm
- Controller capable of synchronized joint updates
- Joint feedback or smart servos
- Rigid base and defined tool center point
- Emergency stop and current-limited supply
Continue building
Download resources
Use these on-page references while working through the project. Downloadable project bundles will be added only after their source and version are published.
Common questions
Frequently asked questions
What is the difference between forward and inverse kinematics?
Forward kinematics calculates the tool pose from known joint values. Inverse kinematics starts with a desired tool pose and searches for one or more joint configurations that can produce it.
Why does a 2-link arm have two solutions (elbow-up and elbow-down)?
For most reachable targets the elbow can bend either way and still place the tool on the same point, giving an elbow-up and an elbow-down configuration. The two solutions come from the plus-or-minus in the law-of-cosines angle for the second joint. They coincide only at a singularity, where the arm is fully stretched or fully folded.
How do I choose between elbow-up and elbow-down?
Pick the configuration that is safest and most efficient for the task: one that keeps joints away from their limits, minimizes movement from the current pose, or avoids obstacles. This simulator lets you toggle between branches and shows the alternate solution as a ghost so the trade-off is visible.
What is a singularity in a robot arm?
A singularity is a configuration where the arm loses the ability to move the tool in some direction—typically when it is fully extended or fully folded. Near a singularity a small tool motion can demand a very large joint motion, so planners slow down or route around these poses. It is also where the elbow-up and elbow-down solutions merge into one.
When does inverse kinematics have no solution?
A planar two-link target is reachable only inside the annular ring between the shortest reach (the difference of the link lengths) and the longest reach (their sum). A point outside that ring cannot be reached at any joint angle. A pose can also be unreachable because it needs a forbidden joint angle, an orientation the available joints cannot achieve, or would collide with the arm itself.
Why use analytic inverse kinematics instead of a numerical solver?
For a two- or three-link planar arm the geometry has a closed-form (analytic) solution, so you can compute the exact joint angles directly, deterministically, and fast—ideal for teaching and testing. Numerical solvers are needed for redundant or spatial arms where no closed form exists, but they iterate, can miss solutions, and are harder to reason about.
Further reading
References
Authoritative sources for going deeper than this simulator's bounded educational model.