# 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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### 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 ...
45 views

### 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 ...
137 views

### 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 ...
91 views

### 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 ...
60 views

### How to calculate twist and wrench in local and global frames

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 ...
87 views

### 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); ...
55 views

### 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 ...
377 views

### 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 ...
152 views

### 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-...
280 views

### 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. ...
177 views

### 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 ...
818 views

### Relationship between the velocity twist Jacobian and the spatial velocity Jacobian

While reading Kevin Lynch's "Modern Robotics" , 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 ...
307 views

### 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 ...
511 views

### 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 ...
500 views

### 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}...
953 views

### 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. ...
493 views