   Free-body diagrams for constrained rigid body dynamics
  Hi all,I have been reading the book "Computational Dynamics" by Ahmed Shabana, and have a few questions.The book talks about creating "free-body diagrams" for constrained rigid multibody dynamics problems.I have attached two examples:The first is a "pendulum with a moving base":which is described in the book as:"Body 1 is a slider block that has a specified motion defined by the function z(t). Body 2 is a uniform slender rod that has mass m2, mass moment of inertia about its centre of mass J2, and length l. The rod that is subjected to the external moment M2 is connected to the sliding block by a pin joint at O."The second,is described in the book as:"The system consists of the ground denoted as body 1, a rod OA denoted as body 2, and a disk denoted as body 3. The rod is connected to the ground by a pin joint at O, while the disk is connected to the rod by a pin joint at A. The rod is assumed to be uniform and its length is l."I have also attached the book's free-body diagrams for these two examples.I'm unclear about how the free-body diagrams are constructed (and it is assumed knowledge in the book).In the first free-body diagram, I understand that m2g (directed down) is the force of gravity, and M2 (anticlockwise) is the externally applied torque. However I am unclear about F12x and F12y, which the book says are the "joint reaction forces at the pin joint".(Similarly I am also unclear about the forces F12x, F12y, F23x and and F23y in the second free-body diagram).I don't understand how the direction of the joint reaction forces is determined (eg why is F12x directed from left to right in both diagrams)?Also, are these directions constant regardless of the orientation of the rod? Or will they change as the rod rotates?Does anyone know of any references that deal with this topic (constructing free-body diagrams specifically for constrained rigid multibody dynamics - particularly describing how to direct the joint reaction forces)? Any reference would be greatly appreciated, as I haven't been able to find an answer to this question so far online or in books.Thanks for your help,Nick.   
  Hi,I am constructional / environmental engineer and I would recommend a book from engineering about static and dynamics. If you speak German you could look at this book here:http://www.amazon.de/Technische-Mechanik-Band-Kinetik-Springer-Lehrbuch/dp/3540684220/ref=sr_1_3?ie=UTF8&s=books&qid=1241511459&sr=8-3 Personally I would look for books from engineering since they are much more practical than theoretical books as Goldstein "Classical Mechanics". Don't get Goldstein as your first book.Cheers,-Dirk   ;  Hi Dirk,Thanks a lot for your reply. Unfortunately I don't speak German, but I will definitely buy a Statics and Dynamics book to learn more about this topic.In the meantime, would you (or anyone out there) be able to answer my original questions about the joint reaction force directions in the Shabana problems?Thanks for your help,Nick.;  The question is too general to answer in my opinion. You need to have a basic understanding of kinematics and dynamic for this.   ;  Understood. Would anyone be able to recommend an English Statics and Dynamics text? I have browsed Amazon and most of the books there seem to have mixed reviews at best. Since the price tag is quite high for these kinds of books, I'd like to make a good investment. :);  Hi Nick,You might find these free online OU courses useful to start you off...Using vectors to model:http://openlearn.open.ac.uk/course/view.php?id=2544Modelling static problems:http://openlearn.open.ac.uk/course/view.php?id=2515To answer one of your specific questions, the F12x F12y values represent the Cartesian components of the unknown joint reaction forces.  The arrows always point in the same direct as they represent x and y components of the unknown joint force vector which could point in any direction depending on the system configuration, but can always be broken down into equivilent x and y components.  See 'Using vectors to model' above for more info on this.I don't have any specific Statics and Dynamics books to recommend, but they generally all cover these topics in much the same way, so I wouldn't worry too much about which one you get.;  I could be wrong, but it sounds like you have a conceptual issue with free body diagrams. If that's the case, continue reading.A free body diagram, or FBD, is ideally a depiction of a single element in a dynamic system. Arrows are drawn to indicate the forces acting upon the element. A FBD should also indicate an established coordinate system. It may also help to draw angles or distances indicating the direction and / or moment through which these forces act on the element. Once the coordinates and all forces are indicated, parallel force components should be summed. The movement (acceleration, to be precise) of the object may then be derived from the sum of forces for each component:a_x = (1/m) (F1_x + F2_x + ... Fi_x)a_y = (1/m) (F1_y + F2_y + ... Fi_y)... etc.Each force is given as a vector. Each torque is given as an angular quantity about a given point. The final acceleration is also a vector. Sometimes the two parts of a FBD (forces / moments versus linear and angular accelerations) are displayed in two separate images, as in http://i42.tinypic.com/6tfwv8.jpg .Some of the examples you are looking at are a little confusing, because they actually consist of several FBDs transposed on top of each other, for multiple elements. I'd recommend considering some simple cases, such as a few coupled masses and springs, first. Sketch the FBDs for each element until you feel comfortable with the dynamics: how each element is effected by forces from the other elements or external factors, how forces and velocities change throughout a system, etc.Hope this helps! I love dynamics and systems, so feel free to ask if there's any questions or confusion remaining.   ;  Hi guys,Thanks a lot for your replies.I've managed to get a hold of some Statics and Dynamics books over the weekend, so hopefully they will help.Just to clarify, I'm familiar with vectors but haven't had any exposure to FBDs before. So would it be correct to say that in FBDs, the unknown vectors (eg the joint reaction force components) are drawn with a direction indicated (eg from left to right for F12x) in the same way as known forces like gravity (mg), even though depending on the configuration, F12x may actually be negative?If this is the case, it seems like the fact that F12x points from left to right in the diagram isn't relevant then, only that it is a horizontal component of the force?So then I was assuming that perhaps unknown force components point in the positive direction (eg left to right for the horizontal component). However this doesn't seem to be the case, as in the second example, there is an unknown horizontal force component pointing in the opposite direction (F23x).I think this is what is confusing me.;  Did you google for FBD? I found this entry at Wikipedia which is a pretty good start:http://en.wikipedia.org/wiki/Free_body_diagramAt the bottom of the page you find a link to a book from Ruina. This is excellent and free. You might want to work through it.@Graham:If you read this you might want to add a link to the book in our reference section. Cheers,-Dirk   ;  Thanks Dirk. The wiki page doesn't address my concern (above), but I'll look into the PDF file.