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Starting at 2:32 of KR210 Forward Kinematics 1 video "d(i) is the distance from X(i-1) to X(i) measured along the Z(i) axis." Therefore the distance from Link 0->1 is d(i), not d(i-1). alpha(i-1) and a(i-1) terms are correct as they measure from (i-1) to (i).