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C00002 00002	∂17-JUL-74  1442		network site SRI
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∂17-JUL-74  1442		network site SRI
 Date: 17 JUL 1974 1441-PDT
 From: PARK at SRI-AI
 Subject: A1*A2*A3...*A6
 To:   LOU at SU-AI
 
 
 LOU:
      PRINT THIS MESSAGE -IT'S LONG.
 
      THE FOLLOWING ARE THE ALGEBRAIC EXPRESSIONS FOR EACH
 OF THE SIXTEEN ELEMENTS OF THE "HAND-POSITION MATRIX"
 IT WAS OBTAINED BY SYMBOLIC MULTIPLICATION OF THE SIX 4X4 FRAME
 MATRICES FOR THE STANFORD ARM.  I USED THE REDUCE PROGRAM
 WRITTEN BY TONY HEARN AT UTAH.  SOME OF THE EXPRESSIONS
 CAN BE FACTORED A LITTLE MORE.
 
 BILL PARK@SRI-AI
 
 COMMENT HAND-POSITION MATRIX FOR THE STANFORD ARM.
 
 A(1,1) =
 
 SIN(THETA1)*(
 
               - SIN(THETA4)*SIN(THETA6)
 
               + COS(THETA4)*COS(THETA5)*COS(THETA6))
 
  + COS(THETA1)*(
 
                  - SIN(THETA2)*SIN(THETA5)*COS(THETA6)
 
                  + COS(THETA2)*SIN(THETA4)*COS(THETA5)*COS(THETA6)
 
                  + COS(THETA2)*COS(THETA5)*SIN(THETA6))
 
 A(2,1) =
 
 SIN(THETA1)*(
 
               - SIN(THETA2)*SIN(THETA5)*COS(THETA6)
 
               + COS(THETA2)*SIN(THETA4)*COS(THETA5)*COS(THETA6)
 
               + COS(THETA2)*COS(THETA5)*SIN(THETA6))
 
  + COS(THETA1)*(SIN(THETA4)*SIN(THETA6)
 
                  - COS(THETA4)*COS(THETA5)*COS(THETA6))
 
 A(3,1) =
 
 
  - (SIN(THETA2)*SIN(THETA4)*COS(THETA5)*COS(THETA6)
 
      + SIN(THETA2)*COS(THETA5)*SIN(THETA6)
 
      + COS(THETA2)*SIN(THETA5)*COS(THETA6))
 
 A(4,1) =
 
 0
 
 A(1,2) =
 
 
  - SIN(THETA1)*(SIN(THETA4)*COS(THETA6)
 
                  + COS(THETA4)*COS(THETA5)*SIN(THETA6))
 
  + COS(THETA1)*(SIN(THETA2)*SIN(THETA5)*SIN(THETA6)
 
                  - COS(THETA2)*SIN(THETA4)*COS(THETA5)*SIN(THETA6)
 
                  + COS(THETA2)*COS(THETA5)*COS(THETA6))
 
 A(2,2) =
 
 SIN(THETA1)*(SIN(THETA2)*SIN(THETA5)*SIN(THETA6)
 
               - COS(THETA2)*SIN(THETA4)*COS(THETA5)*SIN(THETA6)
 
               + COS(THETA2)*COS(THETA5)*COS(THETA6))
 
  + COS(THETA1)*(SIN(THETA4)*COS(THETA6)
 
                  + COS(THETA4)*COS(THETA5)*SIN(THETA6))
 
 A(3,2) =
 
 SIN(THETA2)*SIN(THETA4)*COS(THETA5)*SIN(THETA6)
 
  - SIN(THETA2)*COS(THETA5)*COS(THETA6)
 
  + COS(THETA2)*SIN(THETA5)*SIN(THETA6)
 
 A(4,2) =
 
 0
 
 A(1,3) =
 
 SIN(THETA1)*COS(THETA4)*SIN(THETA5)
 
  + COS(THETA1)*(SIN(THETA2)*COS(THETA5)
 
                  + COS(THETA2)*SIN(THETA4)*SIN(THETA5))
 
 A(2,3) =
 
 SIN(THETA1)*(SIN(THETA2)*COS(THETA5)
 
               + COS(THETA2)*SIN(THETA4)*SIN(THETA5))
 
  - COS(THETA1)*COS(THETA4)*SIN(THETA5)
 
 A(3,3) =
 
 
  - SIN(THETA2)*SIN(THETA4)*SIN(THETA5)
 
  + COS(THETA2)*COS(THETA5)
 
 A(4,3) =
 
 0
 
 A(1,4) =
 
 SIN(THETA1)*(
 
               - S2
 
               + S6*COS(THETA4)*SIN(THETA5))
 
  + COS(THETA1)*(S3*SIN(THETA2)
 
                  + S6*SIN(THETA2)*COS(THETA5)
 
                  + S6*COS(THETA2)*SIN(THETA4)*SIN(THETA5))
 
 A(2,4) =
 
 SIN(THETA1)*(S3*SIN(THETA2)
 
               + S6*SIN(THETA2)*COS(THETA5)
 
               + S6*COS(THETA2)*SIN(THETA4)*SIN(THETA5))
 
  + COS(THETA1)*(S2
 
                  - S6*COS(THETA4)*SIN(THETA5))
 
 A(3,4) =
 
 S1
 
  + S3*COS(THETA2)
 
  - S6*SIN(THETA2)*SIN(THETA4)*SIN(THETA5)
 
  + S6*COS(THETA2)*COS(THETA5)
 
 A(4,4) =
 
 1
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