Constraints for Linkage system

In summary, the individual is asking for help with applying a constraint on a two-dimensional one-bar linkage system. They have solved the equations of motion and noticed that the system can rotate freely 360 degrees, but they want to limit it to only 180 degrees. They are unsure of how to include this constraint in the equations of motion and are wondering if it is correct to only consider the values between 0 and 180 degrees. The conversation also includes a suggestion to use Vise-Grips and hammers for designing, as well as a discussion on the use of Lagrangian methods and impact equations. The expert suggests stopping the first solution at the instant of impact and processing a new initial condition for continued ODE solution, rather than using
  • #1
Ortafux
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Hi guys! I have a question on applying constraint on Linkage systems. Assumed that there is a two dimensional one-bar linkage, one end can only rotate and one end is free (Such as the figure above, please neglect the damper-spring system if you want).
This link can rotate only 180 degrees, not 360 degrees. But when I solve the equations of motion of this system, the animation shows that the system can rotate freely 360 degrees.
I want to know that how it is possible to apply this constraint (rotating only between 0 degree and 180 degrees) in the equation of motion of this link ?
Is it correct to solve the equation of motion and in the end, only consider the value between 0 degree and 180 degrees?!

I would be grateful if you could help me with this problem.
 
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  • #2
There is no way to include the constrain in equation of motion. Assuming that you have correctly solved the equation of motion, it is certainly legitimate to only look at the interval 0<=theta<=pi.

You speak of the animation as though it was something that happened automatically. How did you solve the equation of motion.

By the way, the equation of motion that you would have developed for the motion before the bar hits the wall is no longer valid once the bar does hit the wall. Thus, if you want to be really fussy about the mathematics, you need to substitute a completely different equation of motion for theta>pi.
 
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  • #3
Dr.D said:
There is no way to include the constrain in equation of motion. Assuming that you have correctly solved the equation of motion, it is certainly legitimate to only look at the interval 0<=theta<=pi.

You speak of the animation as though it was something that happened automatically. How did you solve the equation of motion.

By the way, the equation of motion that you would have developed for the motion before the bar hits the wall is no longer valid once the bar does hit the wall. Thus, if you want to be really fussy about the mathematics, you need to substitute a completely different equation of motion for theta>pi.

First of all thank you for your help.
you asked about the way I have solved the equation of motion. I firstly derived the non-linear EOM (Equation Of Motion) and then using numerical methods (like runge-kutta method), got the results and time response (Theta Vs. Time). finally using mathematical softwares ( such as MATHEMATICA) and derived EOM, I plotted the animation of this system.

Do you have any idea to use any equation for Theta>pi ?
 
  • #4
When theta = pi, the equation of motion used for theta<=0 ceases to apply.

At theta = pi, you have to write an impact equation, describing the event of impacting the wall. This will result in a new set of conditions, with theta-dot < 0, and you can then describe the downward swing of the bar until it strikes another constraint.
 
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  • #5
OldEngr63 said:
When theta = pi, the equation of motion used for theta<=0 ceases to apply.

At theta = pi, you have to write an impact equation, describing the event of impacting the wall. This will result in a new set of conditions, with theta-dot < 0, and you can then describe the downward swing of the bar until it strikes another constraint.

Thank you for your reply.

You mean I have to derive the EOM first, after that consider theta-dot < 0 for impact conditions ?! How is it possible to combine this constraint using Lagrangian method ( Or even Lagrangian multiplier method for constraints) ?
 
  • #6
This is why I prefer Vise-Grips and hammers over math when designing things. Just weld a backstrap to the fulcrum above the pivot point on the side opposite your desired arc. When the bar hits it, it ain't going any farther.
By the way, whatever "C" is, you do know that it's not going to experience a straight downward force, right? The connecting rod will just bind or push it sideways.
I know that isn't what you asked about, but it's all that I can determine from the sketch.
 
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  • #7
Actually, there is only one equation of motion, that applies no matter what the sign of theta-dot is. The difficulty is that this equation of motion does not apply at the instant of impact. Thus,
(1) the first solution must be stopped at the instant of impact,
(2) the impact description must be processed to produce new initial conditions,
(3) the same ODE solution is then continued, but with the new initial conditions.

For get Lagrange multipliers, etc. That is just spinning your wheels on this problem.
 
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  • #8
OldEngr63 said:
Actually, there is only one equation of motion, that applies no matter what the sign of theta-dot is. The difficulty is that this equation of motion does not apply at the instant of impact. Thus,
(1) the first solution must be stopped at the instant of impact,
(2) the impact description must be processed to produce new initial conditions,
(3) the same ODE solution is then continued, but with the new initial conditions.

For get Lagrange multipliers, etc. That is just spinning your wheels on this problem.

That's a great approach for this problem. Thank you so much.
 

Related to Constraints for Linkage system

1. What is a linkage system and what are its constraints?

A linkage system is a mechanism that connects two or more rigid bodies, allowing them to move relative to each other. The constraints of a linkage system refer to the limitations or restrictions on the motion of the bodies within the system. These constraints can be physical, such as the shape and size of the bodies, or they can be imposed by the design of the system.

2. How do constraints affect the motion of a linkage system?

Constraints play a crucial role in determining the motion of a linkage system. They limit the degrees of freedom of the system, meaning that the bodies can only move in certain ways. Without constraints, the system would be unstable and unpredictable. Constraints also ensure that the system moves in a controlled and predictable manner, making it useful for various applications.

3. What are the different types of constraints for a linkage system?

The types of constraints for a linkage system can be classified into two main categories: kinematic constraints and force constraints. Kinematic constraints restrict the relative motion between bodies, such as limiting the range of motion or controlling the direction of movement. Force constraints, on the other hand, limit the forces that can act on the system, ensuring that it operates within safe and stable limits.

4. How do engineers design for constraints in a linkage system?

Engineers consider various factors when designing for constraints in a linkage system. They must first understand the purpose of the system and the desired motion or behavior. Then, they use principles of kinematics and mechanics to determine the appropriate constraints that will achieve the desired motion. This involves careful consideration of the geometry, material properties, and external forces acting on the system.

5. What are some real-world applications of linkage systems and their constraints?

Linkage systems with constraints are widely used in various industries, including automotive, aerospace, and robotics. For example, a car's suspension system uses constraints to limit the motion of the wheels and ensure a smooth and controlled ride. In robotics, constraints are used to control the movement of robot arms and manipulators. Linkage systems and their constraints also play a crucial role in machines such as pumps, engines, and turbines, where precise and controlled motion is essential for efficient operation.

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