# A Three-Dimensional Parametric Biomechanical
## 1 Introduction  
It is well-known that motorcycles and bicycles are characterized by a large rider-to-vehicle mass ratio. On motorcycles, this ratio is usually in the range of 0.25-0.35, the lower figure being related to heavy bikes and the upper to sport bikes; while, on bicycles, the ratio is always greater than one. The inertial properties of the rider are, thus, especially relevant when it comes to dynamic simulations, such as those carried out in a multibody environment for handling and stability analyses of the vehicle-rider system [1; 2; 3; 4; 5; 6]. Historically, motorcycle-rider and bicycle-rider systems have been simulated by considering the rider to be rigidly fixed to the chassis, while it has now become standard to consider the rider'suspended' on the chassis (with springs tuned to give the typical frequencies and damping ratios of riders) with their hands interacting with the handlebar [7; 8; 9; 10]. Regardless of the approach (i.e., fixed or suspended rider), estimation of the rider's inertial properties is necessary in both cases. Moreover, in the most advanced motorcycle driving simulators [21; 22; 23; 24; 25; 26; 27], the contribution of the rider's motion on the saddle to the vehicle dynamics are accounted for. Most of the time, such motion is monitored by cameras. The related inertial effects are introduced into the vehicle model after the inertial properties of the rider driving the simulator are assumed. Even in this case, estimation of the inertial properties is relevant. There are different methods to estimate the body segment inertial parameters (BSIP) of a given subject [28; 29; 30; 31; 32; 33; 34], including direct measurements on cadavers [35; 36; 37] or photogrammetry and medical imaging on living humans [38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48]; however, they are more generally estimated by regression and scaling equations (which are derived from such measurements). The inertial properties of the whole body can, then, be computed after defining the subject's posture. A practical approach is to build a three-dimensional multibody model of the whole human body, which consists of the body segments, properly connected to one another. The next step is defining the formulas to be used to estimate the properties of such segments. A number of studies have been reported in the literature focused on the calculation of the inertial properties (e.g., mass, center of mass, moments of inertia, or gyration radii) and lengths of body segments of human bodies using regression/prediction formulas, which are given as functions of the mass and height (see, e.g., Reference [49; 50; 51; 52; 53; 54; 55; 56]). Most of the time, the center of mass is assumed to lie on the longitudinal axis of each body segment, and the longitudinal and transverse axes are assumed principal of inertia. The regression/prediction formulas of body segments in Reference [49] were derived based on the combination of the data sets in Reference [28; 57]: the first considered a sample of American males in the age range of 20-40 years, while the second considered a random selection of adults, young males and females 20-30 years of age, some females in the 40-50 age bracket, and a number of subjects with disabilities in all age ranges. The center of mass was assumed along the longitudinal axis and a single gyration radius was given for each body segment. Nine old male cadavers (average age 69) were used in Reference [50] to estimate the inertial properties of body segments from the human mass and height; a total of 14 body segments were considered (head, trunk, arms, forearms, hands, thighs, shanks, feet). This model is very popular for the two-dimensional estimation of inertial properties of human bodies. The center of mass was assumed along the longitudinal axis, but no moments of inertia were given (as they were deferred to future studies). This paper updates the results of Reference [35], which are still in use (see, e.g., Reference [33]), combined with those of Reference [58].