The length of the last link (1.73) of my model (of a human finger) is not represented in any of the parameters that I calculated using the Denavit-Hartenberg algorithm, which I think can't be right. I suppose it should be represented in either a₃ or α₃, but those are both 0. It should be noted that the model has no end-effector/tool, but I aligned the z₃ with the approach vector anyway. If anyone has an idea where I'm messing up, that would be much appreciated! The model in question:
Note that in your drawing theta_p and theta_d angle are negative according to the right hand rule. That's the first mistake you made, to elaborate, theta_1 is equal to -theta_p.
Also in the last row of your DH table, the translation of DP is in the negative Y direction. Do not forget that the order matters - although there are 5 different combinations of orders of matrix multiplications to calculate the homogeneous transformation matrix.
Forget about the 5 different combinations and stick with the standard one: First rotation about Z Second translation along Z Third translation along X Fourth rotation about X