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I'm 17 years old and learning first-year college math.

  1. What college level math do I need for mechanical linkage design?
  2. Can I learn designing and creating mechanical linkage without math but with my geometric intuition? or there's resource I can upgrade these skill?

It will be very good if you introduce some source textbooks which treat mechanical linkage design.

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    $\begingroup$ Take a look at edx or coursera $\endgroup$ – user8055 Sep 11 '17 at 15:44
  • $\begingroup$ IMO it might be one of the easier topics to approach "intuitively". My course had us playing with lego linkages all the time to try and help see how changes change the system. $\endgroup$ – JMac Sep 11 '17 at 19:50
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    $\begingroup$ Differential equations is the majority of the math side to kinematic chains. To understand how the equations of motion are derived, it would help to know lagrangian mechanics too. $\endgroup$ – Paul Sep 11 '17 at 22:02
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It all depends on how complicated the linkage is. For many simple linkages all you need to know is trigonometry (sin, cos, tan) and torque/moment equilibrium (Force x Distance = Force x Distance). Once you can do this I would say you are in the 95th percentile of linkage design ability. Most non mechanical engineers do not have the ability to calculate or visualize the force transmission of a simple linkage.

If you want to get better and design more complex systems you will need physics 111 and 112 (calculus based). Calculus 1, 2, and 3 are also necessary, mostly 3 because it involves vectors. Statics and Dynamics (200 level engineering courses) tie everything together and reinforce the academic rigor to reliably calculate mechanisms. Machine design (300 or 400 level engineering courses) teach how to add in dynamics, strength of the linkage, inertia, how to simply complex gear systems, optimization, etc.

There are lots of good physics, statics and dynamics books. Probably have a look through a local college bookstore and see what they have (i usually just got the isbn and bought mine used on half.com to save $). Or visit with a professor; they may be able to give you an old copy or point you in the right direction.

Once you have a good trig and physics foundation I would recommend Shigley's Mechanical Engineering Design and the Mechanical Engineering Reference Manual.

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  1. To answer your title, It's not really a matter of what college level, but rather what college. For example, a general studies college (one with a broad range of majors) may not offer such a class, whereas a technical college that focuses specifically on mechanical engineering will offer a variety of these courses at multiple levels.
  2. To answer your first question - a mixture of simple algebra, geometry, and trigonometry are the mathematics required for understanding and designing the more advanced linkages. However, knowledge of physics is also necessary.
  3. To answer your last second question - While it is possible to do this, you will never fully understand the concepts behind it mathematically, and when you do pursue a career in this subject - you may find it very difficult to have a timely workflow without knowing the fundamental basics or the formulas behind it.
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There are some purely geometric linkage design methods, such as two and three position synthesis (which are easy enough to teach even a 8 year old). But there are methods that are not so geometrically intuitive.

The real problem with linkage design is that the mathemathics behind kinematics require a very good foundation of trigonometry and/or imaginary numbers, you know the things that nearly everybody cited as never needing for anything. It is also useful to know linear algebra for coordinate transforms and inverse kinematics calculations.

But even so trigonometric methods only lend themselves to 2D mechanisms. If you want to go further especially into dynamics, then you need multivariable calclulus and larangian mechanics. But beyond basics this gets really nasty, as you have many many singularties. And you end up doing a lot of numerical simulation.

Its one of those things that is deceptively simple at first. Good understanding of statics and equation solving is a plus.

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