solve both, show solution with all steps For gear train shown in Figure, determine the output velocity and center distance of the gear train, where:- N1 = 24- N2 = 36 and Pd = 12- D3 = 2 in and Pd = 10- N4 = 40- N5 = 16 and Pd = 8- D6 = 6 in**Solution:****Diagram Explanation:**The diagram shows a gear train consisting of a series of six gears. The following key components and actions are depicted:1. **Input Gear (ω₁):** This is the initial gear from which the motion starts.2. **Two Intermediate Gears (2 and 3):** These are connected to the input gear and transfer motion through the gear train.3. **Three Additional Gears (4, 5, and 6):** These continue the transmission of motion and include the output gear.4. **Output Gear (ω₆):** This is the final gear where the motion is outputted from the gear train.Each gear is represented by circles in a series, and the interconnected lines indicate the mechanical connection and the path of motion through the gear train.To solve for the output velocity and center distance, calculations involving the number of teeth (N), pitch diameters (Pd), and diameters (D) are required based on the gear train relationships. **Planetary Gear System Analysis****System Configuration:**- **Input:** Carrier (Link 2)- **Output:** Sun (Link 1)- **Fixed:** Ring (Link 6)**Gear Specifications:**- **Gear 1:** Diameter = 1 inch, Pitch Diameter = 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**Problem Statement:**Determine the rotational speed and direction of all members when the input shaft rotates at 1000 rpm counterclockwise (CCW).**Diagram Description:**The diagram illustrates a planetary gear system. It shows the positions of Gears 1, 2, 3, 4, 5, and 6. Gear 4 and Gear 5 are positioned on the same shaft. The carrier (Link 2) is the input, meaning it drives the system, while the Sun (Link 1) is the output. The ring gear (Link 6) is fixed, serving as the stationary part of the system.**Analysis Objective:**Calculate the rotational speed and direction for each component in the planetary gear system given the input conditions.

“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 questions separately.”The value are .Pd is diametrical pitch and N is number of teethCalculation of radius of gear 1 and gear 2Calculation of radius of gear 3 and gear 4Calculation of radius of gear 5 and gear 6Calculation of output velocityCalculation of center distanceThe output speed is The center distance between output and input is .