... S 1 (x 1 , y 1 , z 1 ).Then, using the coordinate transformation from S 1 to S 1 (x 1 , y 1 , z 1 ), we will determinethe normal N 1 and then obtaina 1 = Nx1i 1 + Nz1k 1 . ... SURFACESStep 1: Consider that the worm thread surface (say, the surface side I ) is representedby the vector equation (see Chapter 19 )r 1 (u,θ) = x 1 (u,θ) i 1 + y 1 (u,θ) j 1 + z 1 (u,θ) k 1 , (25.2 .1) and ... ofmeshing.Equations (25.3 .1) and (25.3.2) represent the thread surfaces of the ZK and ZF worms(see Chapter 19 ). The thread profile is located in plane (Fig. 25 .1. 1), and y 1 (uc,θc,ψ) + z 1 (uc,θc,ψ)...