This simulator drives an articulated inspection boom with one yaw joint and two pitch joints. Change the joint angles and link lengths and watch the tool tip move while the lab reports the endpoint computed from the forward-kinematics equations, so you can see exactly how angles compose along the chain.
• A 3D boom on a slewing pedestal at 0.5 m height, with upper boom, forearm and an inspection head, plus an endpoint trace and ground projection. • Sliders for base yaw (-120° to 120°), shoulder pitch (10° to 80°), elbow relative pitch (-100° to 30°), upper link length (0.8-1.8 m) and forearm length (0.6-1.4 m). • Readouts of tool x, y and z, signed horizontal reach and tool pitch, with an option to sweep the shoulder angle automatically. • Preset experiments such as the straight horizontal chain, where the endpoint is (2.2, 0.5, 0) m, and a base rotation that swings the reach into negative world z.
Horizontal reach is r = L1 cos(q1) + L2 cos(q1 + q2) and height is y = 0.5 + L1 sin(q1) + L2 sin(q1 + q2). The base yaw then rotates that reach into the world frame: x = r cos(q0), z = -r sin(q0). The elbow angle is relative to the upper boom, so the forearm's absolute orientation is the sum of shoulder and elbow angles. That is why the elbow changes the tool pitch as well as its position.
The chain is ideal and rigid: no flexibility, no enforcement of joint limits beyond the slider ranges, no collisions and no motor dynamics. Angles are displayed in degrees and converted to radians internally, and the tool orientation simply follows the forearm.
Forward kinematics computes the position and orientation of a robot's tool from known joint values and link dimensions. For a given set of joint angles an ideal serial chain has exactly one answer, which this lab calculates and displays.
The elbow angle is measured relative to the upper boom, so the forearm's orientation in the world is the shoulder angle plus the elbow angle. The inspection head follows the forearm, so its pitch changes with both joints.
Endpoint displacement scales with lever arm length, so the same angular change moves the tool farther when the links are longer. Increase the link-length sliders and compare how far the trace moves for the same shoulder sweep.
Forward kinematics goes from joint values to tool pose and is direct. Inverse kinematics goes from a desired pose back to joint values, may have several solutions or none, and is explored in the companion Inverse Kinematics lab.