I am currently trying to solve a geometric problem where I have to calculate angles in two connected four bar linkages parallel to a serial chain of rotatory joints (closed-loop kinematic chain).
The angle is calculated with
> alpha:=arctan(exp_y, exp_x):
The expressions exp_y and exp_x contain long products of sines and cosines of 6 other time-dependant angles, square roots of these products, constant geometric lengths (not time-dependant) and constant geometric angles (not time-dependant).
The lenghts are already assumed positive
> assume (l1>0): # similar for all lengths l2, l3, ...
The time dependant angles are defined as
> qJ_t := Matrix(6, 1, [qJ1(t), qJ2(t), qJ3(t), qJ4(t), qJ5(t), qJ6(t)]): # generalized coordinates of the system in the sense of technical mechanics
Other assumptions are not set, since the angles can be positive as well as negative.
Calculating this expression takes up to two days on a fast computer. In my opinion this takes much too long compared to other calculations with similar amount of variables (more complex robotic structures).Also, the arctan function does not "calculate" a result, it just writes down "arctan(...)".
Is there a way to speed up this calculation e.g. by using more assumptions?
On the arctan help page, the examples suggest that Maple is trying to already simplify the solution e.g. by drawing Pi out of the solution.