solve both, first one solve for total gear ratio not velocity and second one use table but please use relative velocity instead of x/y and show all setps/solution **Gear Train Analysis**For the gear train shown in the figure, determine the output velocity and center distance of the gear train, where:- \(N_1 = 24\)- \(N_2 = 36\) and \(Pd = 12\)- \(D_3 = 2 \, \text{in and } Pd = 10\)- \(N_4 = 40\)- \(N_5 = 16\) and \(Pd = 8\)- \(D_6 = 6 \, \text{in}\)**Solution:****Diagram Explanation:**The diagram consists of a gear train with six gears labeled from 1 to 6. - **Gears 1, 3, and 5** are on the same shaft.- **Gears 2, 4, and 6** are on different parallel shafts. - Gear 1 takes the input velocity \( \omega_{in} \), transferring motion through the train, concluding with gear 6, which provides the output velocity \( \omega_{out} \). The setup illustrates the mechanical connections showing the sequence of power transmission through physical contact between teeth of adjacent gears. In the following figure, consider the following configuration:- **Input**: Carrier (Link 2)- **Output**: Sun (Link 1)- **Fixed**: Ring (Link 6)**Gear Specifications:**- Gear 1: Diameter = 1 inch, Pitch Diameter (Pd) = 20- Gear 3: 45 teeth- Gear 4: 20 teeth- Gear 5: 30 teeth (keyed to the same shaft as gear 4)- Gear 6: 150 teeth**Task:**Determine the rotational speed and direction of all members when the input shaft rotates at 1000 rpm counter-clockwise (CCW).**Diagram Explanation:**- **Link 1**: Sun Gear, labeled as "1".- **Link 2**: Carrier, labeled as "2", which acts as the input.- **Link 6**: Ring Gear, labeled "6", which is fixed.- Gear 4 is attached to Gear 5, as indicated by the shared shaft.This setup is typically analyzed to understand the gear ratios and directional outcomes in mechanical systems involving planetary gear trains.

“Since you have posted multiple questions, we will provide the solution only to the first question as per our Q&A guidelines. Please repost the remaining question separatelyNow, we have the following data:-where, N1, N2 ,N4 ,N5 are the number of teeths of gears 1, 2, 4 and 5 respectively.Pd2 ,Pd3 Pd5 are the diameteral pitch of gear 2, 3 and 5 respectively.And D is denoting the diameter of gears.So, the total gear ratio is the ratio of angular speeds of output gear and input gear.And the center distance of gear train is the distance between input and output shaft.Determining the radius of gear 1 and gear 2Determining the radius of gear 3 and gear 4Determining the radius of gear 5 and gear 6We have got the number of teeths of gear 6 as N6 = 48 Calculation of output velocityCalculation of center distanceTotal gear ratio of the train is G.R = 1/9 or Center distance of gear train (d) = 1.5 in