Force Analysis without Friction:

Letting that the friction at the hinges does not present. The free body diagrams of link 2, 3 and 4 are illustrated in Figures 9(i), (iii) and (iv), respectively. For given values of F₂ and F₃ the value of F₁ is to be estimated. From these free body diagrams, it becomes obvious that each link contains four or more than four unknowns. These four unknowns may not be estimated by using three equations that are available in a statically determinate structure. However the solution is possible by solving out the problem in parts.

The F₃₄ acting on the link 4, may be resolved parallel to the link and perpendicular to the link  and  estimated, respectively. By taking moments regarding O₄, F₃₄ may be determined

Figure 10(ii) illustrated link 4 and Figure 10(i) illustrated link 3 on which external force F₂ is acting. The forces F₂ and  may be combined to give resultant force R that passes through the point of intersection of  and F₂. Now the link 3 is subjected to R,  and F₂₃ and they need to pass through a pint that is U. F₂₃ passes through A and U. The magnitude of F₂₃ and  may be determined by polygon of forces as illustrated in Figure 10(iii). The forces acting upon link 2 are F₁₂, F₃₂ & F₁. These three forces need to pass through a point 'V' as illustrated in Figure 10(iv). Force F₃₂ = - F₂₃. Hence, force F₃₂ is known and directions of F₁ & F₁₂ are also known. Now the triangle of forces might be drawn and F₁ may be determined. 

(i)                                                                 (ii)

                 (iii)                                                                     (iv)

                        Figure (10)