# Problem in Jacobian matrix

I have a 5DOF robotic arm were 4 joints rotates around a Z axis and one around an x-axis. I am not that good with the Jacobian, but I think I have this. $$J[v,\Omega]=[Z_{i-1}×(O_n-O_{i-1}), Z_{i-1} Z_{i-1}×(O_n-O_{i-1}), z_{i-1} ... Z_{n-1}×(O_n-O_{n-1})].$$

I am a bit confused about Jacobian matrix on the part ($$Z_{i-1}$$), Eg say $$Z_1=[0,0,1]$$. whereby I know that "$$Z$$" is the axis of actuation. What about when one of the joint in my robotic arm rotates around an x-axis does it affect the matrix??

Is it correct to write, $$X_{i-1}$$, eg $$X_1=[1,0,0]$$?

If you do not follow the DH Convention, you can have an actuation axis, which is not Z. In this case it is correct to use $$X_i$$ instead of $$Z_i$$. Your assumption, that is equals $$[1, 0, 0]$$ might be correct. If the $$O$$ matrices are $$4x4$$ in size, then $$X$$ would equal $$[1, 0, 0, 1]$$ (as in this case $$Z$$ would also be $$[0, 0, 1, 1]$$). Also, please make sure that the positive movement (rotation or translation) direction of the motion axis matches the positive direction of the geometrical axis.