Selection of a mechanism highly depends on the end application. Here are some ways to evaluate a mechanism vs your application:
- Input (360 deg rotation in this case)
- Output (180 deg rotation motion in this case)
- Relationship between input and output (mechanical advantage, velocity, and acceleration for a given position). (linear, parabolic, sinusoidal, other crazy polar math, etc)
- Number of moving parts
- Number of rolling surfaces (rollers, gears)(expensive)
- Number of sliding surfaces (pins, slots)(reduced life)
- Number of rotation points (bearing locations)
- Can the mechanism be statically and dynamically balanced (for high speed)
- What is the footprint of the mechanism
- What loads does the mechanism have to endure (material required, fatigue stress, etc)
- Backlash (new and worn)
You may be able to use crank-rocker four bar linkage. I haven't sketched it out, but 180 degrees is likely its theoretical maximum. A spring at either end of the range would help avoid top dead center, but power transfer at those high angles would be difficult. In either example you could replace the orange pin connection with a four-bar. That would eliminate one pin and slot giving you a longer service life.
Four bar linkages are attractive because they employ only low cost rotation connections that have long service lives. Rack and pinion is well suited for when low backlash linear output is required, but can be expensive. Slots and linear bearings are less desirable because of service life, but sometimes reduce the number of components or provide the desired output.