Collaboration diagram for Ship crane:

Kinematics of a crane on a moving base: a rotating base followed by a chain of links, each link with its own length and a pitch joint. The tip position and velocity follow from the base motion, the base angle and the joint angles. The object has no states and does not compute any dynamics: it passes the force at the tip on as the force at the base and gives the torque of that force about the base position.

The base angle \( \phi \) rotates the chain about the base z axis. Joint \( i \) rotates by angle \( \theta_i \) about the y axis of the chain, and link \( i \) points along the x axis of its joint frame with length \( l_i \) (see the code in ShipCrane::Compute for the frames). The angles are in radians (the code takes sin and cos of half the angle); the units of the lengths and rates are not stated in the code.

Input ports

Name	Width	Description
PositionNED	3	Position of the base in the NED frame
VelocityNED	3	Velocity of the base in the NED frame
QuaternionNED	4	Orientation quaternion of the base
OmegaNED	3	Angular velocity of the base. Registered but not used in the calculation
BaseAngle	1	Rotation of the crane about the base z axis
BaseAngleRate	1	Rate of the base angle
ForceNED	3	Force at the tip of the crane
JointAngle \(i\)	1	Angle of joint \( i \), for \( i = 0 \ldots N-1 \) with N = NumberOfJoints
JointAngleRate \(i\)	1	Rate of the angle of joint \( i \)
JointLength \(i\)	1	Length of link \( i \) (an input, so it may change in time)

Output ports

Name	Width	Description
PositionNED	3	Position of the tip in the NED frame
VelocityNED	3	Velocity of the tip in the NED frame
ForceNED	3	Copy of the ForceNED input
TorqueNED	3	The cross product of (tip position minus base position) and the ForceNED input

Configuration parameters

Name	Width	Description
NumberOfJoints	1	Number of joints and links. Integer. Required