Final answer:
A 2-DOF linkage with a quaternary link can be designed using a classic four-bar linkage system, which has four links including the frame and two degrees of freedom when properly configured. While other presented options do not fit the specifications or are not physically feasible, a four-bar linkage is the accurate answer for a 2-DOF linkage with four links.
Step-by-step explanation:
Designing a 2-DOF Linkage with a Quaternary Link
To design a 2-DOF (Degrees of Freedom) linkage with a quaternary (four) link, we can refer to a classic four-bar linkage system. The four-bar linkage is one of the simplest closed-chain mechanisms that can convert rotary motion to linear motion, or vice versa. Considering the question's constraints, let's go through each option provided:
- a) A linkage with two degrees of freedom and four links: This is the correct answer. A four-bar linkage meets the criteria, as it has four links (one being the frame) and typically, two degrees of freedom if properly configured.
- b) A linkage with two degrees of freedom and three links: This would be a three-bar linkage, which typically has only one degree of freedom.
- c) A linkage with four degrees of freedom and two links: This is not physically feasible, as each link typically provides less than four degrees of freedom.
- d) A linkage with one degree of freedom and four links: This could be a four-bar linkage with constrained motion, typically designed for a specific task allowing only one degree of freedom.
For a classic four-bar linkage, we need to ensure that the sum of the shortest and longest links is less than the sum of the remaining two links. This criterion prevents the linkage from reaching a change point, allowing continuous motion. Additionally, the quaternary link, which connects two opposite joints of the linkage, can be designed to accommodate specific lengths and angles, based on the application required.