Questions tagged [screw-theory]
A method of representing the mechanics (kinematics and dynamics) of a system using 6-element vectors (such as a twist or a wrench) which combine both the angular and linear components.
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Lynch, Park derivation of the dynamic equations of motion
In Park and Lynch's "Modern Robotics" textbook (Section 8.2.1), they give the following derivation for the velocity and acceleration of a point $p_i$ with respect to a fixed body frame $\{b\}...
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Screw theory for kinematics/dynamics of mechanisms
Is screw theory commonly used for general kinematics/dynamics of mechanisms (not just robotics)? I'd be interested in anything that covers the types of mechanisms you would find in a typical ...
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Relationship between Lie Algebra (Murray, Lynch) and spatial vector (Featherstone) approaches
I am curious about the relationship between the Lie algebra/group approach to robot kinematics given by Murray (et al.) in "An Introduction to Mathematical Robotic Manipulation" and Lynch (...
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Adjoint representation of twists in the Jacobian derivation
In section 5.1.1 of Modern Robotics by Park and Lynch (pg. 153 of 1st edition, pg. 177 of updated 1st edition), the following derivation is given for the Jacobian matrix.
I don't understand this ...
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How do you calculate this integral term in this PI Controller Formula?
This formula is the PI Control given in Eqn. 11.6, Pg. 419 of Chapter 11 in book Modern Robotics by Kevin M Lynch and Frank C Park.
Here,
Vb is the twist ==> Vb = (angular velocity, linear ...
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v_s quantity in twists
In Modern Robotics v2, we have the following figures:
I don't understand why in Eq. 3.73, we have the given expression for $v_s$. My thinking is:
The position $p$ is the position of the frame $b$ ...
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Articulated Body Algorithm with gear ratio
I am reading up on the proposed articulated body algorithm by Featherstone, which goes like:
Pass 1:
\begin{equation}
\nu_0 = 0\\
\nu_i = {^i}X_{\lambda(i)}\nu_{\lambda(i)}+s_i\dot{q}_i\\
c_i = \nu_i \...
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A single screw axis of a rolling wheel - seems impossible...?
Chasles' theorem:
"Any rigid-body motion can be specified by a rotation about a screw axis and a translation parallel to that axis."
For a rolling wheel, the axis of rotation is ...
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How is Screw Theory used in Robotics when you can do everything with regular kinematics?
I was seeing some Robotics lectures and a word which keeps coming up is "Screw Theory", on looking it up, I find that everything you can do with it practically, you can do with vector ...
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In which frame this wrench is expressed?
Take a look at this question below. The relationship between torques and wrenches are
$$
\tau = J_b^T(\theta) \mathcal{F}_b = J_s^T(\theta) \mathcal{F}_s
$$
where the subscripts $\{b,s\}$ indicate in ...
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Park and Lynch $F = ma$ derivation for a single rigid body
I'm having some conceptual difficulties with a derivation presented in the Modern Robotics text by Park and Lynch. Here are the relevant parts:
At the beginning of the book, they insist that ${\it ...
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3D Rigid Body Pose Optimization in flat euclidean space
I am confused about what is the best way to optimize the 3D pose of an object and the best way to parametrize the translation and rotation for optimization in flat euclidean space.
Assume I have a ...
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what is difference between twist and classcial velocity
In ch 8.2.1 Classical Formulation in the book Modern Robotics by Frank C. Park
I know some remarks about this formula.The origin of coordinate system is coincidence with the mass center of the rigid ...
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perplexity about ch8.2.1 the linear dynamics, in the book <modern robotics>
From previous chapters, I think I have understand the twist, it is about the angular velocity and the linear velocity, the difference is that linear velocity is not one fixed point in the body but is ...
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Calculating wheel linear velocity from body velocity
A frame {b} is attached to the centre of a robot chassis. The planar configuration is given by $(x,y,\phi)$ where $\phi$ is the angle between the x axis in {b} and the x axis of a fixed reference ...
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Forward kinematics confusing point
I am studying robot arm kinematics. In order to construct a transformation from a global coordinate frame to the end effector frame, I have seen references to the Denavit–Hartenberg (DH) convention. ...
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Difference between Denavit-Hartenberg and Rodrigues formulas/conventions
I am trying to compute the forward kinematics for a 6 DOF robot arm.
I've found two methods : the Denavit-Hartenberg (original and modified) and the product of exponentials with the Rodrigues formula.
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Stationary/inertial reference frame
In Modern Robotics by Kevin Lynch, there is a term "stationary" frame, but this is never defined. Googling shows that this is synonymous with inertial frame.
Apparently inertial frame means ...
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Understanding Twists as 3D Velocities
I am just learning about twists to represent 3D velocities (e.g. of a robot's end-effector), and I have two questions:
1) Wikipedia defines a twist as "an angular velocity around an axis and a linear ...
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How to calculate twist and wrench in local and global frames [closed]
I am rather new to screw theory and also lost in robotics books' formulas. we have a simulator of a robot arm within Mujoco physics engine and I'm wondering how I can calculate wrench and twist in the ...
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Screw Axes in the Base Frame
I'm trying to find screw axes for joint (on pic) with angle θ. It's on zero position. As I understood:
joint has an angular velocity on the Z axis, clockwise, so the sign is positive and ω=(0,0,1);
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Velocity description in Screw Motion Theory
As described in the book Modern Robotics by Frank C. Park the velocity of a reference frame can be described as :
$$V_s = J_s(\theta)\dot{\theta}$$
$$V_b = J_b(\theta)\dot{\theta}$$
However in the ...
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Newton-Euler Inverse Dynamics by Screw
I paste this algorithm from textbook Modern Robotics P294 in chapter 8:
This is coordinate invariance of Newton-Euler equations. In the textbook, they use the ...
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The Jacobian resulted from Screw method is different from analytical one (Example Inside)
I am currently solving a kinematics example that asks for the Jacobian. However, when I solve it using the Screw method I get different results from the analytical method, The example is kinda hard to ...
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question about spatial velocity in the book <modern robotics>
I think the equation(3.73) should be:
$\dot p-w_s$x$p=\dot p-\dot p=0$
have no idea how it can be wrong
and don't know the difference between infinitely large body and a body just include the fix-...
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Libraries to calculate kinematics using Screw Theory
Most kinematics libraries/packages use the conventional transformation matrices (DH parameters). However, I'm looking for something that uses Screw Theory principles to set up the Product of ...
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Free-floating sphere dynamics using Roy Featherstone's spatial_v2 toolbox
I am using Roy Featherstone's spatial_v2 to model a mobile robot. I encountered a problem so I went back to modeling a free-floating sphere to familiarize myself with the library and the algorithms.
...
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Kinematics with Product-of-Exponentials terminology: not forward, not inverse
I'm working on a kinematic estimation algorithm, and am trying to come up with the right terminology.
I'm using the Product-of-Exponentials formulation for kinematic chains (and ignoring position ...
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Relationship between the velocity twist Jacobian and the spatial velocity Jacobian
While reading Kevin Lynch's "Modern Robotics" [1], I came across a fundamental question concerning the manipulator Jacobian.
Upon better reading and further cross-checking with Peter Corke's "Robotics,...
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Why using screws instead of homogeneous transforms in kinematics and dynamics?
Can anyone give a justification for using screws (twists, wrenches) instead of the traditional approach (rotation matrices, homogeneous transforms)? Even if screws are more compact, the situation gets ...
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Screw based Jacobian
I am working on kinematics of 5-DOF robot. I already derived geometric Jacobian for position and orientation control.
But for singularity analysis, I require a simplified jacobian. And that can be ...
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Developing world-frame Jacobian using product of exponentials [closed]
I am going through different texts (Spong Robot Modeling and Control, Murray Mathematical Introduction to Robotic Manipulations) and I am seeing different Jacobians developed for the same RRRP ...
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Explanation for exponential coordinate of rotation
From figure above, suppose a three-dimensional vector $p(0)$ is rotated by an angle $\theta$ about the fixed rotation axis $\omega$ to $p(\theta)$. Here we assume all quantities are expressed fixed ...
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Converting product of exponentials from base frame to end-effector frame
This is a homework question from edx course Robot Mechanics and Control, Part II
Given the following
and expressing its forward kinematics as $T = e^{[S_1]\theta_1} ... e^{[S_6]\theta_6}M$
It is ...
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How to find the Adjoint matrix of multiple twists
So let's say I have a three degrees-of-freedom robot with twists ${\xi}_{1}$, ${\xi}_2$, and ${\xi}_3$. The spatial Jacobian is given by
$$
J = \begin{bmatrix}\xi_1 & Ad_{g1}{\xi}_2 & Ad_{g12}...
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Different methods to determine DOF: Chebychev-Kutzbach-Grubler method vs. Screw method
I'm familiar with Chebychev-Kutzbach-Grubler method to determine degree of freedom of a robot arm. But it seems this method fails to calculate the mobility of some parallel robots, as explained here.
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Convert Twist from frame B to frame A [closed]
(full disclosure: this is homework)
I have a twist expressed in frame B:
$\zeta_b = \begin{bmatrix}1\\3\\-2\\0\\-2\\4\end{bmatrix}$
And a general transformation matrix:
$g_{ab} = \begin{bmatrix}-0....
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Robotic manipulator Jacobian by product of exponentials
I've taken a class and started a thesis on robotics and my reference for calculating the Jacobian by product of exponentials seems incorrect, see:
http://www.cds.caltech.edu/~murray/books/MLS/pdf/...
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Adding an Actuator or Force to a (Featherstone) Articulated Rigid Body Model
I'm working on a project where I need to model a system that is essentially comprised of a series of ball-and-socket joints attached to a base, which is attached in turn to a prismatic joint (rail).
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How to find the body jacobain, for each link in a robot manipulator?
The links twist could be obtained, and thus The spatial manipulator Jacobian could be done, but when it comes to the body Jacobian, it is becomes difficult. Moreover, the adjoint transformation ...
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How to get the 4*4 matrix from the twist using product of exponentials, in robot kinematics?
In robot kinematics, we have $e^{(\theta*twist)}$, where $twist$ is 6*1 vector. How do I get the 4 by 4 transformation matrix by using product of exponentials?
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theory on rigid body motion in robotics book
I am reading some theories related to rigid body motion from the book "A Mathematical Introduction to Robotic Manipulation" by Prof. Richard Murray.
I am focusing on chapter 2, Sec 4 to derive some ...
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What is the difference between screw and wrench in rigid body motion?
A screw is defined by a six dimensional vector of forces and torques. It can represent any spatial movement of a rigid body (as written here). But I don't get the following distinction between screw ...
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