Description:

The coordinate system is right hand rule. X cross Y gives Z and Roll is right hand rule about X, Pitch is right hand rule about Y, and Yaw is right hand rule about Z.

Vector Storage:

All linear three vectors (LinPos, LinVel) store their values as [X, Y, Z].
All angular three vectors (AngVel) store their values as [Roll, Pitch, Yaw].
The transformation matrix TM is stored:

Pre-multiplying a local vector by the TM will generate the vector in global coordinates.

Multibody Dynamics, Link Numbers and 60 and 20 Length Vectors:

Please refer to Multibody Dynamics and 60 Length Vectors for information on 60
length vectors.

Methodology:

The spherical models a spherical mechanism.

The spherical takes the input position, velocity, and acceleration from Side 3 adds in the rotational position, velocity and acceleration of the joint and outputs the results on Side 1.

The spherical also takes the internal force and moment from Side 1 and outputs it on Side 3.

Three link numbers are requested from the multibody solver and these are added to the list of link numbers in LinkNumber3 and output in LinkNumber1.

The spherical calculates the torque generated about the joint due to the perturbation of each degree of freedom. In addition it calculates the default torque due to gravity, velocity, and external forces.

The multibody solver calculates the actual joint acceleration, which is integrated and output in JointAngRate and JointAng. Euler parameters are used in the joint to avoid any singularities.
 

SimRealVar Force1[60] - Global Force (N)
SimRealVar Moment1[60] - Global Moment (Nm)

Outputs:

SimRealVar LinAccel1[60] - Global Linear Acceleration (m/s/s)
SimRealVar LinVel1[3] - Global Linear Velocity (m/s)
SimRealVar LinPos1[3] - Global Linear Position (m)
SimRealVar AngAccel1[60] - Global Angular Acceleration (rad/s/s)
SimRealVar AngVel1[3] - Global Angular Velocity (rad/s)
SimRealVar TM1[9] - Transformation Matrix (ND)
SimRealVar LinkNumber1[20] - Link Number Output (ND)
 

SimRealVar LinAccel3[60] - Global Linear Acceleration (m/s/s)
SimRealVar LinVel3[3] - Global Linear Velocity (m/s)
SimRealVar LinPos3[3] - Global Linear Position (m)
SimRealVar AngAccel3[60] - Global Angular Acceleration (rad/s/s)
SimRealVar AngVel3[3] - Global Angular Velocity (rad/s)
SimRealVar TM3[9] - Transformation Matrix (ND)
SimRealVar LinkNumber3[20] - Link Number Input (ND)

Outputs:

SimRealVar Force3[60] - Global Force (N)
SimRealVar Moment3[60] - Global Moment (Nm)
 

SimRealVar ExternalJointTorque - External Joint Torque (Nm)

Outputs:

SimRealVar JointAng[3] - Joint Angle (rad)
SimRealVar JointAngRate[3] - Joint Angular Rate (rad/s)
 

Outputs:

SAngVel[3] - Global Angular Velocity (rad/sec)
EulerParm[4] - Euler Parameters (N/D)
 

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