Barrett WAM Arm - Table 6 - Joint Limits; Equation 3 - Tool Frame Matrix; Equation 4 - Tool End Tip Position and Orientation Equation for the 4-Dof Wam; Equation 5 - Tool End Tip Position and Orientation Equation for the 7-Dof Wam

WAM Arm – User’s Manual support@barrett.com www.barrett.com
© 2008 Barrett Technology®, Inc. Document: D1001, Version: AH.00 65 of 80
Each of the joints has a mechanical stop that limits the motion. Refer to Table 6 below for a
complete listing of the joint limits for each axis.
Table 6 – Joint Limits
Joint Positive Joint Limit
Rad (deg)
Negative Joint Limit
Rad (deg)
1 2.6 (150) -2.6 (-150)
2 2.0 (113) -2.0 (-113)
3 2.8 (157) -2.8 (-157)
4 3.1 (180) -0.9 (-50)
5 1.24 (71) -4.76 (-273)
6 1.6 (90) -1.6 (-90)
7 3.0 (172) -3.0 (-172)
Forward Kinematics for the 4-DOF WAM
The forward kinematics of the 4-DOF WAM system is used to determine the end tip location and
orientation. These transformations are generated using the parameters in Table 4 on page 64 and
the matrix in Equation 1 on page 64.
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
=Τ
1000
4
zzzz
yyyy
xxxx
Tool
pwvu
pwvu
pwvu
Equation 3 – Tool frame matrix
You define the
Tool
Τ
4
frame for your specific end-effector. The forward kinematics are
determined for any frame on the robot by mulitplying all of the transforms up to and including the
final frame. To determine the tool end tip location and orientation use the following equation:
ToolTool
ΤΤΤΤΤ=Τ
4
4
3
3
2
2
1
1
00
Equation 4 – Tool end tip position and orientation equation for the 4-DOF WAM
Forward Kinematics for the 7-DOF WAM
As with the previous example, you define the
Tool
Τ
7
frame for your specific end-effector. The
forward kinematics are determined for any frame on the robot by mulitplying all of the transforms
up to and including the final frame. To determine the end tip location and orientation use the
following equation:
ToolTool
ΤΤΤΤΤΤΤΤ=Τ
7
7
6
6
5
5
4
4
3
3
2
2
1
1
00
Equation 5 – Tool end tip position and orientation equation for the 7-DOF WAM