14
votes
Accepted
How is Screw Theory used in Robotics when you can do everything with regular kinematics?
Screw theory greatly simplifies the notation and expressions used. This allows for complex systems to be considered. As an added bonus it completely eliminates the need to specify which coordinate ...
- 383
8
votes
Relationship between the velocity twist Jacobian and the spatial velocity Jacobian
There are a lot of definitional problems and inconsistencies in this area.
Geometric Jacobian. I'm not sure this has a precise and agreed upon meaning. But across the more classical robotics books (...
- 1,692
6
votes
Accepted
question about spatial velocity in the book <modern robotics>
A coordinate transformation of a point P from Frame 1 to Frame 0 is given by:
$$
\mathbf{p}^0=\mathbf{o}^0_1+\mathbf{R}^0_1\mathbf{p}^1.
$$
Differentiating with respect to time gives:
$$
\dot{\mathbf{...
- 3,995
5
votes
Screw based Jacobian
The geometric Jacobian provides all the information you need for singularity or manipulability analysis. Linearly dependent columns correspond to joints with parallel axes. More information about ...
- 1,692
4
votes
Explanation for exponential coordinate of rotation
The author expects a background that includes a course in physics or mechanics where this equation is taught. When that is the case, this equation gives you instantaneous velocity of a particle (point)...
- 4,385
4
votes
Accepted
Robotic manipulator Jacobian by product of exponentials
The Jacobian in that equation is from the joint velocity to the "spatial velocity" of the end effector.
The spatial velocity of an object is a somewhat unintuitive concept: it is the velocity of a ...
- 619
4
votes
Accepted
Why using screws instead of homogeneous transforms in kinematics and dynamics?
About why screw axes:
According to Kevin Lynch in his video of Twists, "just like the time-derivative of a rotation matrix is not equivalent to the angular velocity, the time-derivative of a ...
- 156
4
votes
The Jacobian resulted from Screw method is different from analytical one (Example Inside)
You're computing the spatial Jacobian, which relates joint velocities to spatial velocities at the origin. You instead want to compute the body Jacobian, which relates joint velocities to end-effector ...
3
votes
Stationary/inertial reference frame
Due to the way that frames are defined in the Modern Robotics book (and in this type of vector-field mechanics in general, such as those of Featherstone), both the spatial frame and the body frames ...
3
votes
Velocity description in Screw Motion Theory
The body velocity $V_{b}$ is the velocity of the frame with respect to the world, as seen from the frame's perspective. Its rotational component $\omega_{b}$ contains the rotation rates around the ...
- 619
3
votes
Accepted
Libraries to calculate kinematics using Screw Theory
Lynch and Park's Modern Robotics book uses the product of exponentials formula and screw axes to describe manipulators, and they have a well-documented library available in Python, MATLAB, and ...
- 3,760
3
votes
Accepted
Different methods to determine DOF: Chebychev-Kutzbach-Grubler method vs. Screw method
I will try not to skip too many steps. Assuming a Global coordinate frame at the base and the arm is fully extended along the Y-axis of the base frame.
Since SCARA has four joints, we will create ...
- 103
3
votes
Accepted
Convert Twist from frame B to frame A
Hint: First, write the transformation matrix as
$$
T = \begin{bmatrix}
R &p\\0_{1\times3} &1
\end{bmatrix}.
$$
Now we use the relations $\omega_a = R\omega_b$ and $q_a = Rq_b + p$. Then since $...
- 1,829
3
votes
Accepted
Articulated Body Algorithm with gear ratio
In Featherstone's book "Rigid Body Dynamics Algorithms", there is a section of Chapter 9 (specifically, 9.6) dedicated to explaining how to incorporate gears into a given dynamic model.
At a ...
2
votes
Accepted
Explanation for exponential coordinate of rotation
First note that
$p(0)$ travels along an arc of the circle of radius $r = \Vert p \Vert \sin(\phi)$ centered at a point on the axis of $\omega$; and
the velocity $\dot{p}$ is perpendicular to the arc ...
- 1,829
2
votes
Accepted
How to find the Adjoint matrix of multiple twists
You want to use the product of exponentials to calculate the transformation of $\zeta_1$ and $\zeta_2$ for $\theta_1$ and $\theta_2$.
To be more clear, using your notation of $g_{12}$:
\begin{...
- 101
2
votes
How to find the body jacobain, for each link in a robot manipulator?
Worked example
$\hspace{2.5em}$ $\vec{q}$ = $[q_{1}\hspace{1em}q_{2}]^{T}$ $\hspace{1.5em}$ [Generalized coordinate]
$\hspace{2.5em}$ $\vec{J}$ = $\frac{\partial \vec{r}_{OA}(\vec{q})}{\partial\vec{...
- 143
2
votes
Screw based Jacobian
Adding to Peter Corke's answer, there's also a Coursera course by Kevin Lynch which uses the Modern Robotics book as a reference and explains how to derive the screw based Jacobian. The Jacobian can ...
- 323
2
votes
Free-floating sphere dynamics using Roy Featherstone's spatial_v2 toolbox
You still haven't posted the (full) code that gives the results you've presented; when I run your snippet I don't the results you posted. Instead, I get:
...
- 16k
2
votes
Newton-Euler Inverse Dynamics by Screw
maybe need some transformation from centers of mass to the joint frame?
Isn't that what $A_i$ is? I don't have the book with me, but from your excerpt:
Let $A_i$ be the screw axis of joint $i$ ...
- 16k
2
votes
The Jacobian resulted from Screw method is different from analytical one (Example Inside)
There are in fact two types of Jacobians, a geometric Jacobian and an analytical Jacobian. The intro to chapter 3 in the book: Robotics: Modelling, Planning and Control by Bruno Siciliano, Lorenzo ...
Ben♦
- 5,825
2
votes
How is Screw Theory used in Robotics when you can do everything with regular kinematics?
Screw theory is another way to describe the motion of rigid bodies. The difference between this theory and the homogenous transformation matrix (i.e. standard approach) is the fact that with the ...
- 2,453
2
votes
In which frame this wrench is expressed?
Edited Answer
From the question, it seems the loading is applied at the end effector but its line of action along the $x_s$ direction.
I do prefer to resolve everything on the world inertial frame ...
- 383
2
votes
Forward kinematics confusing point
The author of the referenced thesis is using exponential coordinates and screw theory via the Product of Exponentials formulation to generate the sequence of transformations from one link to the next.
...
2
votes
How is Screw Theory used in Robotics when you can do everything with regular kinematics?
Why use polar or spherical coordinates when you can use Cartesian coordinates for everything? Why use Laplace transforms to solve differential equations?
I think most of the challenge in higher math ...
- 16k
2
votes
How do you calculate this integral term in this PI Controller Formula?
The term $X_e$ is not a matrix in SE(3) but a twist, as defined in the paragraph following the equation where it states that "... the configuration error $X_e(t)$ is not simply $X_d(t)-X(t)$, ...
1
vote
Difference between Denavit-Hartenberg and Rodrigues formulas/conventions
The DH method requires you to carefully specify local frames attached to each link and calculate linear and angular offsets between those frames in a very specific way in order to reduce the effective ...
1
vote
Accepted
Park and Lynch $F = ma$ derivation for a single rigid body
The key thing to remember is that none of the equations used in the Modern Robotics textbook use "body-fixed frames". The {b} frame is defined as a "body frame" which is ...
1
vote
Accepted
3D Rigid Body Pose Optimization in flat euclidean space
See https://www.cis.upenn.edu/~cjtaylor/PUBLICATIONS/pdfs/TaylorTR94b.pdf.
You can absolutely use "flat" Euclidean space based optimizers while also optimizing on the manifold, but I agree ...
- 449
1
vote
Accepted
what is difference between twist and classcial velocity
In these equations from Modern Robotics (by Park and Lynch), the fixed inertial frame ${b}$ is both the reference frame used to define all of the coordinate vectors and has its origin located at the ...
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