4. The figure below shows a simple bicycle model where the forward motion of the bicycle...

 

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4. The figure below shows a simple bicycle model where the forward motion of the bicycle is in the positive XR direction and the origin is centred on the rear wheel of the bicycle. The distance between the centres of the two wheels is 1m and the radius of both wheels is 0.3m. The front wheel is steerable and is currently turned at an angle of radians. r = 0.3mi XR r = 0.3m /4 (i) 1 = 1m Write down the rolling constraint for each of the wheels. (ii) Write down the inverse differential kinematics for the platform. (iv) If a third fixed wheel is added to the bicycle inline and to the rear of the back wheel, as shown in the figure below, what will be the effect of this third wheel on the degree of mobility of the platform? Explain your answer. (v) r = 0.3m r = 0.3mi 1=1m XR 1=1m r = 0.3m /4 Using the Rank / Nullity approach described during lectures, compute the mobility, steerability, and maneuverabilty of the updated platform. What is your interpretation of your results? 4. The figure below shows a simple bicycle model where the forward motion of the bicycle is in the positive XR direction and the origin is centred on the rear wheel of the bicycle. The distance between the centres of the two wheels is 1m and the radius of both wheels is 0.3m. The front wheel is steerable and is currently turned at an angle of radians. r = 0.3mi XR r = 0.3m /4 (i) 1 = 1m Write down the rolling constraint for each of the wheels. (ii) Write down the inverse differential kinematics for the platform. (iv) If a third fixed wheel is added to the bicycle inline and to the rear of the back wheel, as shown in the figure below, what will be the effect of this third wheel on the degree of mobility of the platform? Explain your answer. (v) r = 0.3m r = 0.3mi 1=1m XR 1=1m r = 0.3m /4 Using the Rank / Nullity approach described during lectures, compute the mobility, steerability, and maneuverabilty of the updated platform. What is your interpretation of your results?