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Appendix B - Motor-to-Joint Position Transformations
The following transformations show the change in joint positions as a function of motor
positions. The input transmission ratios and the differential transmission ratios are calculated
from known pulley, pinion, and cable diameters.
 −1
0

N
 1
 Jθ 1  
1


0

2N 2
 Jθ 2 
 Jθ  = 
− n3
 3  0
 Jθ  
2N 2
 4 
 0
0


0 

 Mθ 0 
0 
 Mθ 
 1 
0  Mθ 2 
 Mθ 
 3
1 

N 4 
0
−1
2N 2
− n3
2N 2
0
Equation 3: Arm Motor-to-Joint position transformations
 N 1   35.87 
  

 N 2   28.21
N  = N 
 3  2 
 n3   1.68 
 N   17.77 

 4 
Equation 4: Arm transmission ratios
 1

 Jθ 5   2 N 5

  − n6
 Jθ 6  = 
 Jθ   2 N 5
 7 
 0

1
2N 5
n6
2N 5
0

0 
 Mθ 4 


0  Mθ 5 


− 1  Mθ 6 
N 7 
Equation 5: Wrist Motor-to-Joint position transformations
Barrett Technology, Inc.
BA4-310 System User Manual Version 1.1
70