AN EMB-145 FLT CREW DEVIATED FROM CHARTED HDG ON AMRST1 DEP FROM CLE; CITING CONFUSION BETWEEN CHARTED PROCS AND CONFLICTING ATC INSTRUCTIONS.

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CLRED FOR TKOF ON RWY 6R VIA AMRST1 DEP 360 DEG HDG. AS PER THE INITIAL CLB SEGMENT FOR RWY 6R WHICH STATES 'CLBING L TURN TO DJB VIA DJB R-082 TO 2600 FT THEN VIA ASSIGNED HDG TO 5000 FT OR ASSIGNED ALT' WE TURNED TO INTERCEPT THE RADIAL UNTIL 2600 FT. CLBING THROUGH 2000 FT; ATC QUERIED ABOUT OUR HDG AS THEY EXPECTED 360 DEGS. THEY STATED THAT THERE IS MUCH UNCERTAINTY ABOUT THE DEP (EVEN ON THEIR PART) AND ASKED THAT WE FILE A RPT TO BRING ATTENTION TO THIS. I FEEL THAT WE FOLLOWED THE PROC EXPLICITLY.SUPPLEMENTAL INFO FROM ACN 703964: WE RECEIVED OUR CLRNC FROM CLE AND WE WERE GIVEN AMRST1 DEP; VWV TRANSITION. THEN AS FILED; MAINTAIN 5000 FT; 280 DEGS 10 AFTER; 128.25; SQUAWK XXXX. WHEN WE WERE GIVEN TKOF CLRNC FROM TWR FOR RWY 6R WE WERE ALSO GIVEN A HDG OF 360 DEGS. AFTER TKOF WE COMPLIED WITH THE AMRST1 DEP WHICH STATES; 'CLEVELAND-HOPKINS INTL: RWYS 6L/R; 10: CLBING L TURN TO DJB R-082 TO 2600 FT THEN VIA ASSIGNED HDG TO 5000 FT OR ASSIGNED ALT.' AFTER TKOF WE MADE A CLBING L TURN TO INTERCEPT THE DJB R-082 UNTIL WE PASSED 2600 FT AT WHICH POINT WE THEN TURNED BACK R TO OUR ASSIGNED HDG OF 360 DEGS GIVEN TO US BY THE TWR. THERE WAS CONFUSION BETWEEN OUR FILED CLRNC AND THE TWR ASSIGNED HDG. ALSO HOTTER THAN USUAL AMBIENT TEMPS COMBINED WITH A HVY LOAD CAUSED US TO HAVE TO CONTINUE OUR TURN TO INTERCEPT PRIOR TO REACHING 2600 FT. AFTER MAKING OUR TURN BACK TO THE 360 DEG HDG; DEP CTLR ASKED US OUR ASSIGNED HDG. WE CONVEYED OUR ASSIGNED HDG AND THAT WE WERE COMPLYING WITH THE AMRST1 DEP. DEP CTL INFORMED US THAT THERE WAS A DISCREPANCY AND ASKED US TO FILL OUT A RPT AS IT WAS APPARENT THAT WE WERE NOT THE FIRST TO DO THIS. NO FURTHER ACTION WAS NEEDED AND WE WERE ADVISED BY DEP THAT NO CONFLICT HAD OCCURRED.