Questions tagged [kinematics]

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Relation between links and pairs in Kinematic chain

I came across a equation for kinematic chain (for lower pairs only) : L = 2P-4 where L: Number of Links; P is the number of pairs how could this equation be derived ? EDIT: I tried putting values in ...
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13 views

How to show that the total angular velocity vector of a rigid body is the sum of all angular velocity vectors acting on it

I am trying to prove the additivity propety for the angular velocity vectors acting on a body in three dimensions. Particularly also in the case when the axes of rotation do not cross each other (the ...
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34 views

Linearisation of the Equations of Motion of an Inverted Double Pendulum

I am working to develop a deep reinforcement learning model for balancing an inverted double pendulum. To do so, I needed to derive the equations of motion, via the Euler-Lagrange (EL) method and now ...
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18 views

Sprocket Angular Velocity [duplicate]

I have a question please that I need help on. Consider the chain that is draped over the sprocket with mass moment of inertia of 0.005kgm^2 about central axis. If 4kg block is released from rest from ...
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1answer
64 views

To stop or to go around?

Let us we are moving in a car. There is a wall in front of us, we need to decide can we go around it or not. It is known that width of the wall is $w$ and our speed is $v = const$. What is a simple ...
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58 views

In circular motion , why do we say this is centripetal acceleration

Let us say a particle is moving in a circle with Uniform circular motion . Then , if I take an equation like this . $\theta$ = S(Arc length or Total distance covered ) / Radius of circle *( time ...
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2answers
36 views

Did not understand this regarding angular velocity

It says $V\sin \alpha$ (component of velocity perpendicular to OP) is the cause of angular displacement. How is it? if only $V\cos \alpha$ existed, we need not turn over head to always to look at a ...
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2answers
101 views

Degrees of Freedom for Complex Pulley Systems

I'm trying to understand DOF clearly, but this pulley system has me doubting myself. When I try to determine the degrees of freedom, I sum the DOF of each object, and subtract the constraints. for ...
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1answer
96 views

Center of rotation (rigid body)

I know the meaning of (instantaneous) “center of rotation” and “center of zero acceleration” for a rigid body. I know that they do not coincide (in general) and that their positions change with the ...
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2answers
183 views

Rotational Motion Kinematics - Not sure how to fix axis of rotation

Hi I am trying to make a CAD model of something like the scoop sampler shown below. http://www.rolls-royce.com/~/media/Files/R/Rolls-Royce/documents/customers/nuclear/scoop-sampling-tcm92-50918.pdf ...
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1answer
46 views

Gear Ratio of a Stepped Planetary Gearset

I was looking into planetary gearsets, and came upon the concept of a stepped planetary gearset. In the image shown above, if my input was the blue sun gear, the output was the planet gear, and the ...
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1answer
99 views

Dynamics of a rigid body in a system of two linear drives

I've been trying to solve the dynamics of this system for quite a while, but cannot seem to get the right answer. I've tried solving it with Lagrangian method but I am not so confident with the ...
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1answer
531 views

Deriving the equations of motion for free-floating spacecraft with a single link robot arm

Note: I had previously posted this question on the Space and Robotics SE sites, but received little/no response. So I've deleted the previous posts and repasted my question here in the hope of ...
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1answer
83 views

How to compute the size of a polygon moving along non-circular guide rails

I am trying to compute the optimal (a non-optimal solution would also work) size of carts that can move along guiding rails. Each cart is connected to the rails at two points. Each cart is also ...
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11 views

3DOF end effector control

I have created a simple serial robot with some servos and CAD. Each joint has 180 degrees of freedom, where they all have 180 degrees of freedom. I haven't specified where the 180 degrees of freedom ...
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1answer
24 views

differential drive vehicle in screen coords

differential drive vehicle in world frame what would change in the kinematic model of the differential drive vehicle if i wanted to simulate it using pygame module in python ( pygame or opencv or any ...
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Problem in the inverse kinematic model of a car like vehicle?

I'm a electrical engineering student and i am building a simulation of a car like vehicle . As I understand it: The input for the forward kinematic model are the control variables and the output is ...
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1answer
32 views

Stewart platform 6DOF parrallel manipulator static force diagram

I am trying to develop a statics free body diagram of a stewart platform 6dof parallel manipulator motion table. I have the base points (B1,B2,B3,B4,B5,B6) and the top platform points (P1,P2,P3,P4,P5,...
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What do I need to operate this motor?

I am currently designing a tennis ball launcher. I am looking to use the friction wheel approach, where you have the ball passing through 2 spinning wheels and being launched by the frictional force. ...
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2answers
56 views

What does it mean for a machine design to be “kinematic”?

I've seen the term "kinematic" used qualitatively to describe machines several times in books and on YouTube. I think I understand what kinematics is as a study, but I'm not sure what people ...
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1answer
30 views

Euler rotations and acceleration

I have a system determined by 3 Euler angles that describe the orientation with respect to a fixed coordinate system XYZ. The angular velocioties are: $\omega_2$ (precession), $\omega_1$ (nutation) ...
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2answers
145 views

How to interpete the formula: $I_{G}\alpha = \dot{\vec{H}}$?

I am having hard time to fully undestand what those formula's actually mean. I know the meaning of each element: I : moment of inertia H : angular momentum $\alpha$: angular acceleration $\omega$: ...
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0answers
25 views

How to measure / calculate Tait-Bryan angles of a moving platform in SimMechanics

I exported a model of the mechanism created in SolidWorks to SimMechanics in order to explore the possibilities of control. To solve the problem, i need to know the angular position of the mobile ...
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1answer
36 views

Maximum velocity of an athlete [closed]

I was solving a mechanics sum An athlete running a 100m run starts from rest and reaches the maximum speed in a distance of 15 m. He runs the remaining distance with that velocity and reaches the ...
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2answers
9k views

Calculating torque needed to climb a graded hill

I've been designing an electric skateboard which is driven by only one of the rear wheels (for the moment). As I was picking out motors for the board, I soon realized I would need to find a balance ...
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1answer
19 views

Purpose of normalization of Jacobian in a parallel manipulator

I am currently studying a robotics paper, where a normalized frobenius norm of a matrix is calculated as part of determining the condition number of the corresponding linear system of equation: $\...
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1answer
33 views

I have the yaw rate, rear wheel speeds, and the radius of tires, how to find x and y speeds?

I only have these 3 data sets: rear right and left wheel speeds (they change with time) yaw rate (also changes with time) constant dynamic rolling radius How am I supposed to find the directional ...
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1answer
284 views

Inertia relief in ANSYS - rotating model

I'm trying to use ANSYS to solve statically a dynamic problem. As shown in the image below, there is an orange bar that is constraint to slide horizontally only and attached to another bar (pink) ...
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1answer
51 views

How do I call a kinematic assembly that converts rotary motion to sawtooth linear?

I have in mind a device somewhere in between a firearms trigger and a clock escapement. One way it could be constructed is as follows: A crank would displace a linearly moving slider backwards, so ...
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1answer
12k views

GIM Mechanism Software (Kinematics / Analysis / Synthesis)

I've recently discovered a very awesome software tool for the synthesis and analysis of mechanisms. The tool is called GIM, from Faculty of Engineering in Bilbao, Department of Mechanical Engineering,...
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1answer
961 views

Deformation gradient, strain tensor from cylindrical coordinates

I do not have any engineering background but I am studying some mathematics to try and understand and solve this problem. I have a mesh (M1) in cylindrical coordinates and this deforms into a mesh (M2)...
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1answer
775 views

What are displacement field and Deformation field?

I am studying mechanics of materials while I came across these terms called the displacement fields and the deformation fields. I am not able to understand the difference between them. Can someone ...
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1answer
205 views

Designing cylindrical cam

So I need to design a cylindrical cam (aka barrel cam I think). I'm an aerospace engineer so I've never had a course on cams/gear design (wish I had though). Is there a general equation for the curve (...
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1answer
115 views

Moment of Inertia of a Rotor System

I need to settle a discussion on the following question: Part A: Find the equivalent spring constant for springs in series Use equations of motion, sum of torques to find natural frequency of the ...
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1answer
396 views

4 Gears in a Circular Pattern - Calculating the Proper Distances for Meshing

I have recently been working on a gearbox for a robot. I have this pattern of 4 gears with each gear connected to its 2 neighbors. It looks like this: You will probably notice something though. ...
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1answer
44 views

Torque computation for different attachment point

I have a pretty basic question but I would like to be sure of what I think. I have a setup like the one in the figure. I have two motors which can generate two forces $F_1$ and $F_2$ perpendicular ...
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1answer
107 views

Bending Moment Doubt

I don't understand how bending moment is being calculated in the problem mentioned in the above link. I understand the parts after that i.e. calculating elastic potential and partial derivatives but I ...
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0answers
1k views

How to calculate the coupler length in a crank rocker mechanism

I'm trying to learn a bit about building kinematic mechanisms by building a small project. The goal is to be able to open and close a box programmatically via a servo motor. I have a small box that ...
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2answers
2k views

What is meant by “shock load” in gears?

What is meant by shock load in gears? What are steady, light, medium and heavy shock loads?
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49 views

No. Of Instantaneous centres

I’m reading “Theory of Machines and Mechanisms” by Joseph Shigley. Page No. 118 - The author states that A mechanism has as many instant centres as there are ways of pairing the link numbers. Thus,...
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52 views

Rotating four cylinders with one motor/actuator

I have a setup with 4 cylinders placed next to each other in following configuration. The cylinders are made of .2mm stainless steel. I would ideally want to rotate them along their axis using a ...
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1answer
74 views

Unachievable motions because of singular Jacobian

This is the Jacobian of a robot arm (IBB IRB 120) with already specified joint angles (0,0,0,0,0,0). This Jacobian is singular for this configuration. ...
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333 views

Inverse kinematics solutions pros and cons

I know at least 3 different approaches to solve inverse kinematics problem. They are pseudo inverse jacobian, cyclic coordinate descent and ANFIS networks. I would like to know advantages and ...
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3answers
154 views

Compound gear system: Finding velocity

In the figure below we have that the gear $A$ is has an fixed axis and has the radius of $R_a = 0,1m$ and, in the instant represented in the figure spins clock-wise with angular velocity $\omega_a = 4\...
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1answer
170 views

Kinematics Mechanics Find the length of the belt and the speed of the rack

For A. I know that the formula for belt is simply $L=\frac{Pi(D_a+D_b)}{2}+2C+\frac{(D_b-D_a)^2}{4C}$ Which gives me $L= 116.99"$ since C is equal to $50$ For B. However I'm stuck and can't get the ...
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2answers
167 views

Questions on machinery terminology

I have some questions in the basics of machinery terminology Can a spring ever be a link? Most books (eg. Ham et al. 58, Shigley pg. 5) consider links to be rigid. However, I have come across ...
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918 views

Forward and Inverse Kinematics of PUMA 560

I am currently coding a Forward and Inverse Kinematics solver for a PUMA 560 robot. For the Inverse Kinematics part I am using the closed for solution given in this paper. But my issue is, my solution ...
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98 views

force transmission in kinematic chain

In the following kinematic chain, I would like to get equation to go from $F_{in}$ to $T_{out}$. (excuse the poor drawing, nodes 3,4,5 are always aligned) Here's my attempt : The torque at $1$ is : $...
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2answers
215 views

Universal joint vs Double Universal Joint (CV configuration) kinematics

Concerning this subject, I consulted the following Wikipedia page: Universal joint where the elementary kinematics equation of the U-joint is stated. But, a little bit further in the article Double ...
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3k views

Feedback control of two-link planar manipulator

TL;DR: how can I calculate the disturbance at each joint due to coupling forces in a two-link planar robot manipulator actuated by two independent DC motors? I'm studying control theory and trying to ...