7

You are right he made a mistake there. This is probably one of many typos in this preprint of Mark Spong. You should rather turn to other good books, such as the mathematically more elegant book of Richard Murray,Zexiang Li and Sankar Sastry, A Mathematical Introduction to Robotics Manipulation (MLS94). The mathematics they use is consistent in other of ...


7

Craig uses the modified DH parameters, while Spong uses the classic DH parameters. The difference between them are the locations of the coordinates system attachment to the links: in the modified DH, the coordinates of frame $O_{i}$ is put on axis $i$, while in the classic DH convention the coordinates of frame $O_{i}$ is put on axis $i+1$. Update (2014....


6

I have been doing a lot of reading up on kinematic calibration and here is what I found: From [1]: A kinematic model should meet three basic requirements for kinematic-parameter identification: 1) Completeness: A complete model must have enough parameters to describe any possible deviation of the actual kinematic parameters from the nominal values....


6

Your professor has made an error, but he or she is only human. The upper-left 3x3 matrix must be an orthonormal rotation matrix. Every column of that must have a unit norm. The second column $[0, 1, -1]^T$ has a norm of $\sqrt{2}$ which makes the rotation matrix invalid.


5

Here is the traditional way. I think this is the kinematics of your arm, but am not 100% sure. Here are the DH parameters and transformation matrix: DH Parameters for the anthropomorphic arm with spherical wrist $$ \begin{array}{c c c c c} \\\hline \text{Link} & a_i & \alpha_i & d_i & \vartheta_i \\\hline \\1 & 0 & \...


5

The updated image solves the problem. You did not consider the end-effector coordinate frame earlier. Also, the crosses (going into) in the diagrams should be replaced by dots(coming out), because the crosses don't hold the right hand rule in case you are using a right hand coordinate system.


4

The link, What are the advantages of using the Denavit-Hartenberg representation?, in Paul's comment provides a correct synopsis. Additional, practical benefits are: DH provides a guaranteed minimal representation. Very good for linear algebra computations, as you want to use the most compact form that's available. DH matrices are very straight-forward to ...


4

You will need to provide target coordinates (x,y,z, etc) to your inverse kinematics equations. As long as they have the same scale as your DH parameters, the joint angles calculated will be the same. But since you don't know the scale factor, you don't know how to scale your inputs.


4

Add a coordinate system that matches the previous coordinate system exactly. The last rotary joint will be the parameter for the next-to-last coordinate system, and the link length will be the parameter for the prismatic joint. Note: a simpler approach is possible, but this gets the job done easily.


3

Unfortunately it is not as simple as just shifting the a and alpha columns, as the locations of the frames and the directions of their axes can also change when moving from one DH formulation to another. As you can see in the Wikipedia entry on Modified DH Parameters, these key differences result in a number of changes to how the overall transformation ...


3

You should read this paper: "Lipkin 2005: A Note on Denavit-Hartenberg Notation in Robotics". It explains the 3 main DH parameter conventions and how they differ.


3

In DH, the Z axis always goes along the direction of variability. For a rotational (revolute) joint, that means Z is the axis of rotation. For a translational joint (prismatic) the Z axis is in the direction that the joint can translate. For each direction the robot can be actuated, a coordinate system is needed. So your example of a gantry crane, if that ...


3

They are two different ways of getting the same thing. Correctly set D-H parameters will give the exact same kinematics and dynamics as correctly set POE parameters. There are well-defined (although tedious) ways to convert between the two. So "better" or not purely is up to user preference. Some people prefer D-H because for many setups they give a unique ...


3

Ah ha! From my comment earlier - If it's kinematics, then none of the joints are a function of any of the other joints. The only exception is if you had a kinematic loop, like a four bar mechanism, or a rocker, or a crank. What you have is a four bar mechanism, and it has probably been giving you trouble because: It's just a hard problem to begin with, ...


3

I changed the code and now it works properly. rob.Xtree{1} = rotx(1.57) * xlt([0 0 0]); rob.Xtree{2} = roty(1.57) * xlt([0.15,0,0]); rob.Xtree{3} = xlt([0.34 0 0]);


2

This is Best Youtube video which gives thorough explanation of Denavit Hartenberg Algorithm and Parameters Forward Kinematics: Denavit-Hartenberg Convention Following is youtube channel by Prof. Yang Cao from University of British Columbia which covers all topics in Advanced Robotics. This is best place for learning robotics concepts for Robotics ...


2

You don't need an explicit declaration for X, Y, and Z because the information is all relative to the previous joint. For a terrific tutorial, see this video. You don't typically use DH parameters to generate a transform from one fixed coordinate to another fixed coordinate; you use them to define joint motions. In your example, you want to recreate the ...


2

I recently worked with DH parameters to define kinematics of my Dual Arm Robot. As per my knowledge and experience, for kinematics I can say that DH Param will be good to use it since that gives you exact location and orientation (provided the table you made is correct) of each link of the robot. I had to work for collision detection between both the arms of ...


2

The Denavit-Hartenberg parameters $(r,\alpha,d,\theta)$ (according to here) actually depicts rigid displacement of a directed point-line (i.e. a line with a particular point selected on it, where the origin of the local frame is located) in space, bearing in mind that coordinate frames are set up in such a way that $r,\alpha$ is about x-axis and $d,\theta$ ...


2

In general, Euler angles (or specifically roll-pitch-yaw angles) can be extracted from any rotation matrix, regardless of how many rotations were used to generate it. For a typical x-y-z rotation sequence, you end up with this rotation matrix where $\phi$ is roll, $\theta$ is pitch, and $\psi$ is yaw: $R = \begin{bmatrix} c_\psi c_\theta & c_\psi s_\...


2

Khalil himself says that it is a form of the modified D-H parameters. See, e.g., Section 2.1 of the 2000 Springer-Verlag book Advances in Robot Kinematics.


2

Here are the step that are in my course for using D-H convention: Step 1 Define the z axis of every joint Step 2 Define the origin frame R0 (O0, x0, y0, z0) Step 3 For i in [1, n] (n=number of joint) Step 3.1 Define Oi that belongs to zi, and to the common normal to zi-1 and zi Step 3.2 Define xi such as xi is normal to the plan formed by zi-1 and ...


2

The geometric method of computing inverse kinematics (which you are calling the trigonometric way) and the Denavit-Hartenburg method result in the same kinematic equations. Neither is better, although DH can be generalized more easily to suit a variety of arm geometries. Regarding which algorithm is faster, it depends on how you implement the equations ...


2

The solution of the inverse kinematics problem and the Denavit Hartenberg method (or algorithm) are two very different things. The DH provides rules on how to define coordinate systems, but it does not constrain or guide to on how to solve the inverse kinematics problem. These are two distinct steps. Setting the coordinate systems The DH method is used to ...


2

The easiest way to validate a set of DH parameters is to plug them directly into a simulator which can build a robot model from a DH table. Once you've got the DH-generated robot model, you can verify that the robotic structure that is generated is what you would expect based on your DH table. The most common DH-table based robot simulation package that I'...


2

You are correct in the sense that you just need an extra transformation from your world frame to the first frame (fixed) in you D-H parametrization. This transformation might be fixed or time varying (if you consider a mobile base robot for instance), but is not part of the D-H parametrization. In other words, your D-H parametrization describes the ...


2

The steps to define a frame for the DH parameters are the following: $Z_n$ axis in the direction of motion of joint $n-1$ $X_n$ axis such that it is perpendicular to both $Z_n$ and $Z_{n-1}$ and runs from $Z_{n-1}$ to $Z_{n}$ (this defines the origin). The special case here is when both Z axes are parallel and thus there are infinite solutions. In this case,...


2

The DH parameters comes from the common normal between two consecutive Z axes. Every time you're in doubt about the DH parameters, you can follow common guidelines between two consecutive axes. In this case, $d_i$ is the distance along previous Z starting from the previous origin O to the intersection of the new X and previous Z axis, which is variable in ...


2

I'm not sure where you went wrong, but that's because you haven't explained how you arrived at your DH values or how you converted from DH to rotation matrix. This question doesn't really need all that, though, because the axes are swapped but otherwise remain colinear. If you were trying to get to/from O3 it'd be a bit harder. The matrix, any matrix but ...


2

There are 2 main rules in assigning frames following DH convention: source: Robot Modeling and Control, Spong et. al $x_i \perp z_{i-1}$ $x_i$ intersects $z_{i-1}$ In your attempts, Your first attempt is incorrect as your $z_2$ axis is not in the direction of actuation of the prismatic joint. I'm not clear on your second attempt as $x_1$ appears to be ...


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