This is a picture of Master Andrew, my youngest son, ridding on one of his favorites at the park near our home, the “wild ducky”. 

In the back you can also see his other favorite, the “bucking bronco”.  The picture was taken a few years ago, when I used to carry my camera everywhere I went, and take a picture of every single smile, frown or bugger.  Andy’s summer break started several weeks ago, so we’ve been to that park quite a bit already. He still likes the bronco, but I don’t take that many pictures anymore.

Anyway, watching him ride one of those got me thinking of running a little motion study, just for fun.  That’s how I came up with my own version of the bucking bronco that you see here and used a linear spring to simulate the bouncing movement.

Granted, this is extremely simplified. The real bronco doesn’t only bounce up and down, but also bends back and forth and side to side, as the child pushes and pulls and shifts his or her weight during the ride. I definitely don’t think I can simulate that using this particular spring, because for once, this is not even a model of the spring, but only a simulation element, and also because bending the model of a spring in such a fashion would most likely involve some significant deformation and SolidWorks Motion considers all components in the motion study to be rigid.  That would be a whole different kind of study!

In the meantime, this is what can be done with what’s available…  I modeled the bronco as a single part just to make my life easier.  As you can see, my assembly has only two components: the bronco and a square base that represents the ground where the ride will be attached to. The linear spring will be placed between these two parts, but keep in mind that it’s not a real component so the spring itself isn’t enough to guarantee the movement will always go according to plan.

While preparing my assembly for the study, I added a coincident mate between the front planes of both the bronco and the base, another coincident mate between the right planes of the same two components, and a distance mate to position the bottom of the bronco twenty inches above the base. When creating the new motion study, however, I eliminated the distance mate from the study, while still leaving it in the model.  This is done easily from the Motion Manager, thanks to the fact that SolidWorks Motion allows you to have what it’s known as local mates.  Local mates are mates that are added to or deleted from that motion study exclusively, without affecting the model or any other motion study you may have.  To add, delete or suppress a local mate, always do it from the Motion Manager, while in the motion study tab of interest.  If you then click on the model tab and look at the mates folder, you’ll see that they haven’t been affected by any local mates you applied in your study.  

Now, about that spring…  Adding a spring to a motion study is not so hard. Choose the motion study mode to be Motion Analysis and click on the spring icon to add a spring. You will see a property manager appear on the left, where you will have to specify certain parameters for your spring. The first one has to do with the kind of spring you want to add, which in this case is a linear spring. Next, you will have to specify the spring endpoints; you can do this by selecting a point, an edge or a face for each endpoint of the spring. I used a couple of faces.  The idea behind applying those two coincident mates was to center the bottom of the bronco above the square base. This is because I used the rectangular face of the bronco’s bottom and the top face of the square base to define the endpoints of the linear spring.  Each endpoint was positioned right at the center of each of the faces I chose.  By making sure that the faces are centered with respect to each other, I also made sure that the spring would go straight along the Y axis.

As soon as the endpoints are specified, the free length of the spring is calculated as the distance between the two endpoints. If you leave it like that, it means your spring isn’t preloaded. You can change it, however.  If you increase the value, then it means your spring is already under compression. If you decrease the value, then your spring is already under tension, because in that position it’s stretched out beyond its free length. This is important to keep in mind because the spring will tend to go back to its original free length and will then exert a force on the components that it connects, bringing them closer or pushing them apart. In my case, I wanted a spring that wasn’t preloaded and had a free length of twenty inches, and that was the purpose of the distance mate I added to the model in the beginning. I deleted this mate from the study, however, because it was simply to position the bronco.

The spring constant is part of a relationship that describes the dependency between force and displacement and in this case is 1, for a linear spring.   The spring rate  is also part of the same spring relationship between force and displacement and can be described, for simplicity, as the amount of force needed to compress a spring a certain distance, or more specifically, how many pounds of force are required to compress the spring by one inch. Springs that have a low spring rate are said to be soft, while springs that have a higher spring rate are said to be stiffer. This only means that it takes a bigger load to compress a stiffer spring by one inch than it would take to compress a softer spring.  Here is the spring relationship for the linear spring:

F = -K(X-Xo) + Fo

Where:

            X = Distance between the two locations that define the spring

            Xo= Reference length (at preload)

            Fo= Reference force of the spring (at preload)

            K= spring stiffness coefficient also known as spring rate

            F= spring force

Some springs have two values listed for their spring rate. This means that the spring starts at one rate and ends at a different rate throughout compression, like in the case of a step linear spring or a progressive spring. I believe it’s possible to simulate this kind of springs in Motion, but I haven’t tried.

Back to defining the spring for the bronco…  Trying to figure out a spring rate for this example was a bit tricky at first.  By default, Motion starts with a value of 1, but if you add gravity to this example and run the study, you’ll discover that with that value this spring isn’t even able to bounce back and/or support the weight of the bronco at all. It needs to be much stiffer than that. I ended up with a spring rate close to 10 and it seems pretty decent.  

Under Display in the spring property manager you will be able to enter values for the coil diameter, the number of coils and the wire diameter. While these values have real impact on the spring rate in reality, here they are merely for display purposes and won’t affect the result of the simulation.

If you add gravity in the negative Y direction and run the simulation with this spring, you’ll see the bronco bouncing up and down by the effect of its own weight for what seems to be an eternity, but we all know that springs in the real world don’t bounce forever, because they all have some sort of structural damping built in and that’s what that damper field in the spring property manager is for.  

For my bronco, I used a linear damper and played with different values between zero and one for the damping constant.  By creating a plot of the displacement of the bronco in the Y direction against time (measured with respect to the global coordinate system), I was able to observe the effect of the damper constant in the simulation more clearly.  This plot shows the displacement of the bronco when a damper constant of 0.1 is used. 

This other plot shows the displacement of the bronco when a damper constant of 0.4 is used. As you can see, the higher the constant, the faster the bronco comes to a stop.

After the bronco had stopped completely, I added an action only force in the negative Y direction to the top of the seat to simulate a small child seating on the ride.  This is the new displacement plot after running this simulation.  Notice how the second time the bronco comes to a stop it does at an even lower position than before.

These studies are highly simplified, I know, but they still have some educational value. I hope to learn more about Motion and Simulation soon, or at least enough to come up with more complicated examples.