Galileo Sphere Robot (GSR) Kinematics
ROBOT KINEMATICS FOR GALILEO SPHERE ROBOT
Robot definition as a group of axes with a predefined point type
The robot kinematics will be assigned to a new model type (15) with a XYZPR (x,y,z, pitch, roll) point type. The following line defines the GALILEO robot as a new system variable:
Common Shared GALILEO As Group Axnm = A1 Axnm = A2 Axnm = A3 Axnm = A4 Axnm = A5 model = 15 of xyzpr
Kinematics of the robot
Joint Coordinates:
Axis name Joint Type Range Units Theta1 J1 Rotary axis [-180,180] deg Theta2 J2 Rotary axis [-10,90] deg Z1 J3 Linear [Z1min,Z1max] mm Z2 J4 Linear [Z2min,Z2max] mm Theta3 J5 Rotary axis Multi turn deg
There are three rotary axes:
• theta1 – big horizontal rotary (J1 or joint #1) • theta2 – pitch axis (J2 or joint #2) • theta3 – tool rotation (J5 or joint #5)
And two linear axes:
• Z1 (J3 or joint #3) • Z2 (J4 or joint #4) The Z1 is the linear axis without connecting rod. General presentation of the robot joint point in MC-Basic language is (list of numeric expressions inside curly brackets):
{J1, J2, J3, J4, J5}
Cartesian coordinates:
Cartesian coordinates (world) of the robot TCP (Tool Center Point) are (Xw, Yw, Zw). Orientation of the robot tool’s Z axis is always expressed as a rotation needed to rotate the Z world (Zw) axis into Z tool (Zt) axis. It can be expressed with 3 Euler angles (Yaw, Pitch, Roll) of the ZYZ order of rotations.
Yaw angle:
Rotating (Xw, Yw, Zw) system around Zw axis into (X1, Y1, Z1)
Pitch angle:
Rotating (X1, Y1, Z1) system around Y1 axis into (X2, Y2, Z2)
Roll angle:
Rotating (X2, Y2, Z2) system around Z2 axis into (X3, Y3, Z3) which coincides to (Xt, Yt, Zt)
As the given robot has only 5 DOF (Degrees Of Freedom) we are reducing the orientation representation to Pitch & Roll angles only. That corresponds to rotations around Y2 (axis obtained after rotating Yw with θ1) and Z3 tools Z axis (in that order).
General presentation of the robot Cartesian point in MC-Basic language is (list of numeric expressions inside curly brackets preceded with hash sign):
- {X, Y, Z, Pitch, Roll}
